Lesson Plan | Traditional Methodology | First Degree Equations

Objectives

Duration: (10 - 15 minutes)

The aim of this lesson plan stage is to clearly present the learning objectives to the students, providing an overview of what will be covered during the class. This helps to guide the students' focus and ensures they understand the importance of the content to be studied, as well as preparing them for the practical examples that will be discussed.

Main Objectives

1. Understand the concept of first-degree equations and their practical applications.

2. Learn to solve first-degree equations in the form ax + b = c, using the properties of equality.

3. Apply the acquired knowledge to solve everyday problems, such as taxi fare calculations.

Introduction

Duration: (10 - 15 minutes)

The purpose of this lesson plan stage is to contextualize the students about the topic, showing the relevance of first-degree equations in practical everyday situations. This not only sparks students' interest but also prepares them to understand the importance of the subject, facilitating the connection between theoretical content and its real-life applications.

Context

To start the lesson on first-degree equations, begin by explaining that equations are mathematical tools that help us find unknown values. Give simple, everyday examples, such as calculating the amount of ingredients in a recipe or determining the change in a purchase. Highlight that first-degree equations are the most basic and essential for solving many everyday problems. Using a story or situation that students can easily relate to can be a good strategy to capture their attention.

Curiosities

Did you know that first-degree equations are frequently used in economics to calculate the cost of products or services? For example, when using transportation apps like Uber or 99, the fare is usually calculated with a fixed fee added to a variable that depends on the distance traveled. Understanding these equations can help them better understand how these charges are made and even plan their personal finances.

Development

Duration: (40 - 50 minutes)

The purpose of this lesson plan stage is to provide a detailed and practical understanding of first-degree equations. By addressing fundamental concepts, properties of equality, and steps for solving, students will have a solid foundation for solving equations. Additionally, application to real-life problems, such as taxi fare calculations, helps to contextualize the knowledge, making it more relevant and easier to understand.

Covered Topics

1. Concept of First-Degree Equations: Explain what a first-degree equation is, highlighting that it is a mathematical expression in the form ax + b = c, where 'a', 'b', and 'c' are real numbers and 'x' is the variable we want to find. 2. Properties of Equality: Detail the properties of equality (addition, subtraction, multiplication, division), which are fundamental for solving equations. Explain that what is done on one side of the equation must also be done on the other side to maintain equality. 3. Steps to Solve First-Degree Equations: Explain the steps to solve a first-degree equation. Include practical examples to illustrate each step, such as isolating the variable 'x', simplifying the equation, and solving the equation to find the value of 'x'. 4. Practical Examples and Applications: Show examples of everyday problems that can be solved with first-degree equations. Explain in detail how to set up the equation from the problem and how to solve it. Use examples like taxi fare calculation, where the fare consists of a fixed fee and a variable based on the number of kilometers traveled.

Classroom Questions

1. Solve the equation: 2x + 3 = 11. Explain each step you took to find the value of 'x'. 2. A taxi charges R$ 5.00 as a base fare (fixed fee) plus R$ 2.00 per kilometer traveled. Write the equation that represents the total cost of a ride of 'x' kilometers and calculate the cost for a 10-kilometer ride. 3. During a promotion, a store offers a fixed discount of R$ 20.00 on any purchase and also a 10% discount on the purchase value. If the original price of an item is R$ 100.00, what is the final price after applying the discounts? (Tip: Create an equation to solve the problem).

Questions Discussion

Duration: (25 - 30 minutes)

The purpose of this lesson plan stage is to review and consolidate the knowledge gained by the students, ensuring they have correctly understood the concepts and steps for solving first-degree equations. A detailed discussion of the answers and reflective questions encourage critical thinking and practical application of knowledge, in addition to promoting active participation from the students.

Discussion

• Solve the equation: 2x + 3 = 11. Explain each step you took to find the value of 'x'. First, subtract 3 from both sides of the equation to isolate the term with 'x': 2x + 3 - 3 = 11 - 3, resulting in 2x = 8. Next, divide both sides of the equation by 2 to find the value of 'x': 2x/2 = 8/2, resulting in x = 4. Therefore, the value of 'x' is 4.

• A taxi charges R$ 5.00 as a base fare (fixed fee) plus R$ 2.00 per kilometer traveled. Write the equation that represents the total cost of a ride of 'x' kilometers and calculate the cost for a 10-kilometer ride. The equation that represents the total cost is C = 5 + 2x, where 'C' is the total cost and 'x' is the number of kilometers traveled. For a 10-kilometer ride, substitute 'x' with 10: C = 5 + 2(10), resulting in C = 5 + 20, so C = 25. Therefore, the total cost of the ride is R$ 25.00.

• During a promotion, a store offers a fixed discount of R$ 20.00 on any purchase and, in addition, a 10% discount on the purchase value. If the original price of an item is R$ 100.00, what is the final price after applying the discounts? (Tip: Create an equation to solve the problem). First, apply the fixed discount of R$ 20.00: 100 - 20 = 80. Then, calculate the 10% discount on the new value: 10% of 80 = 0.10 * 80 = 8. Subtract the percentage discount from the resulting value: 80 - 8 = 72. Therefore, the final price of the item after the discounts is R$ 72.00.

Student Engagement

1. Did anyone find a different answer to the first question? If so, where do you think the error might have occurred? 2. Regarding the second question, can anyone think of a different situation where this formula could be applied? 3. For the third question, how would you handle a situation where the percentage discount is applied before the fixed discount? Would the answer be different? 4. Do you think that understanding how to solve these equations could help in other areas of life? Can you give examples?

Conclusion

Duration: (10 - 15 minutes)

The purpose of this lesson plan stage is to review and consolidate the main contents covered, connecting theory to practice and reinforcing the importance of the topic for the students' daily lives. This moment is essential to ensure that students leave the class with a clear and practical understanding of the concepts learned.

Summary

• Concept of First-Degree Equations: First-degree equations are mathematical expressions in the form ax + b = c, where 'a', 'b', and 'c' are real numbers and 'x' is the variable we want to find.
• Properties of Equality: Addition, subtraction, multiplication, and division are properties that maintain the equality of an equation.
• Steps to Solve First-Degree Equations: Isolate the variable 'x'; Simplify the equation; Solve the equation to find the value of 'x'.
• Practical Examples and Applications: Everyday problems, such as taxi fare calculation, can be solved with first-degree equations.

The lesson connected the theory of first-degree equations with practice by using examples like taxi fare calculation, where students could see how an equation in the form ax + b = c is applied to calculate real costs. This approach helped students understand the utility of equations in practical everyday situations.

Understanding first-degree equations is important for everyday life, as they are used in various daily situations, such as calculating expenses, planning finances, and understanding service charges. For instance, when using transportation apps or making purchases with discounts, knowledge of this type of equation helps make informed and accurate decisions.