Lesson Plan | Technical Methodology | First Degree Equation

Objectives

Duration: 10 to 15 minutes

The purpose of this stage is to provide students with a clear understanding of first-degree equations and their practical application. This is fundamental not only for academic success but also for preparing students for real situations in the job market, where the ability to solve mathematical problems in a practical and efficient manner is highly valued.

Main Objectives

1. Understand and solve first-degree equations, such as 2x-3=5, in a practical and efficient manner.

2. Apply knowledge of first-degree equations to solve everyday problems, such as comparing the costs of services offered by two different companies.

Side Objectives

1. Develop critical thinking and problem-solving skills.
2. Promote collaboration and teamwork through practical activities and challenges.

Introduction

Duration: 10 to 15 minutes

The purpose of this stage is to provide students with an initial understanding of the topic and engage them through practical and relevant examples. This creates a meaningful context for learning and establishes the importance of first-degree equations in real situations and in the job market.

Contextualization

First-degree equations are present in various situations in our daily lives. From simple calculations, such as determining the price of a product with a discount, to more complex decisions, such as planning a monthly budget. Understanding and solving these equations is an essential skill that facilitates decision-making and the resolution of practical problems.

Curiosities and Market Connection

Did you know that many professionals in the job market use first-degree equations daily? Engineers, economists, and financial analysts often solve equations to predict costs, maximize profits, and minimize expenses. For example, a market analyst may use these equations to determine the break-even point between a company's fixed and variable costs, helping to optimize production and increase profitability.

Initial Activity

Start the class by presenting a provocative question: 'How can we determine which phone carrier offers the best value for our cell phone plan?' Then, show a short video (2 to 3 minutes) that illustrates an everyday situation where solving a first-degree equation is necessary to make an informed decision.

Development

Duration: 60 to 65 minutes

The purpose of this stage is to deepen students' understanding of first-degree equations and their practical application. Through interactive activities and challenges, students develop problem-solving, critical thinking, and teamwork skills. The fixation exercises and assessments ensure that students can apply the concepts learned independently.

Covered Topics

1. Concept of first-degree equation
2. Isolating the variable
3. Solving equations of the type ax + b = c
4. Application of first-degree equations in everyday problems
5. Comparison of fixed and variable costs

Reflections on the Theme

Guide students to reflect on how first-degree equations are used in different professions and in everyday financial decisions. Ask how the ability to solve these equations can influence their personal and professional choices. Facilitate a discussion on the importance of understanding and applying mathematical concepts in practical situations.

Mini Challenge

Practical Challenge: Comparing Phone Plans

Students will be divided into groups and given information about two phone plans from different carriers. Each plan has a fixed cost and a variable cost per minute of use.

Instructions

1. Divide the class into groups of 3 to 4 students.
2. Provide each group with a table of the fixed and variable costs of the phone plans.
3. Ask the groups to write and solve the first-degree equations to find the point at which the two plans have the same cost.
4. Guide students to discuss which plan is more advantageous for different usage patterns (low, medium, and high consumption).
5. Each group must present their conclusions to the class.

Objective: Apply knowledge of first-degree equations to solve a practical problem and develop critical analysis and teamwork skills.

Duration: 30 to 35 minutes

Evaluation Exercises

1. Solve the following first-degree equations:
2. 3x + 5 = 20
3. 7x - 4 = 31
4. 2(x - 3) = 4
5. 5x/2 + 3 = 13
6. Practical problem: An internet service company offers two plans. In Plan A, the cost is R$ 50.00 fixed plus R$ 2.00 per gigabyte used. In Plan B, the cost is R$ 30.00 fixed plus R$ 4.00 per gigabyte used. Write and solve the equation to find the point at which the two plans have the same cost. Which plan is more advantageous for different levels of usage (10GB, 20GB, 30GB)?

Conclusion

Duration: 10 to 15 minutes

The purpose of this stage is to consolidate learning, ensuring that students understand how to apply theoretical concepts in practical situations. This stage also promotes reflection on the importance of the topic, encouraging students to recognize the value of the skills acquired for both academic success and professional life.

Discussion

Guide students to reflect on the concepts learned, discussing how first-degree equations were applied in comparing phone plans and how these skills can be useful in other everyday and professional situations. Facilitate a discussion on the challenges faced during the exercises and how practice helped solidify understanding.

Summary

Recap the main content presented in the lesson, including the concept of first-degree equations, the process of isolating the variable, solving equations of the type ax + b = c, and the practical application of these equations in everyday problems, such as comparing fixed and variable costs.

Closing

Explain to students how the lesson connected mathematical theory with practical applications, highlighting the importance of understanding and solving first-degree equations to make informed decisions in various areas. Emphasize the relevance of this knowledge in the job market and daily life, promoting critical analysis and problem-solving skills.