Lesson Plan | Technical Methodology | Quadratic Equation: Bhaskara

Objectives

Duration: 10 - 15 minutes

The purpose of this stage is to ensure that students understand the importance of solving quadratic equations, not only as a mathematical concept but as a practical skill that can be applied in various situations in the job market, such as in engineering, economics, and technology. Developing these practical skills is essential to prepare students for real-life challenges and enhance their employability.

Main Objectives

1. Solve quadratic equations using Bhaskara's formula.

2. Apply Bhaskara's formula to solve practical problems.

Side Objectives

1. Identify the coefficients of a quadratic equation.
2. Understand the concept of the discriminant and its implications for the solutions of the equation.

Introduction

Duration: 10 - 15 minutes

The purpose of this stage is to ensure that students understand the importance of solving quadratic equations, not only as a mathematical concept but as a practical skill that can be applied in various situations in the job market, such as in engineering, economics, and technology. Developing these practical skills is essential to prepare students for real-life challenges and enhance their employability.

Contextualization

Quadratic equations are present in various everyday situations and have a wide range of practical applications. For example, in civil engineering, they are used to calculate the strength of materials, and in economics to model the behavior of financial markets. Understanding how to solve these equations is fundamental for anyone interested in pursuing a career in areas that involve calculations and predictions.

Curiosities and Market Connection

An interesting curiosity is that Bhaskara's formula, which many learn in school, was developed over a thousand years ago by Indian mathematicians. In the job market, these equations are used in various fields, such as in physics to calculate the trajectory of objects, in computer graphics to render images, and even in artificial intelligence for algorithm optimization.

Initial Activity

To spark students' interest, show a short video (3-4 minutes) that visually and animatedly explains how Bhaskara's formula can be applied to calculate the trajectory of a rocket. After the video, ask the following provocative question: 'How do you think Bhaskara's formula can help determine the trajectory of a rocket or predict the behavior of the financial market?'

Development

Duration: 60 - 65 minutes

The purpose of this stage is to ensure that students are capable of applying Bhaskara's formula in practical situations, developing essential skills for the job market. The proposed activities encourage collaboration, problem-solving, and effective communication of results, preparing students for real challenges.

Covered Topics

1. Identification of coefficients a, b, and c in the quadratic equation.
2. Calculation of the discriminant (Δ) and interpretation of its values.
3. Application of Bhaskara's formula to find the roots of the equation.
4. Discussion about the relevance of quadratic equations in the job market.

Reflections on the Theme

Guide students to reflect on how mathematics can be a powerful tool for solving real-world problems. Ask how they think companies utilize quadratic equations in their daily operations. Facilitate a discussion on the importance of mathematical skills in developing technological solutions and making strategic business decisions.

Mini Challenge

Practical Challenge: Building a Launch Parameter

Students will be divided into groups and tasked with creating a simplified model of projectile launch using Bhaskara's formula to calculate the point of impact. They will need to identify the coefficients a, b, and c from a provided practical situation and calculate the discriminant to find the roots representing the launch and impact points.

Instructions

1. Divide the class into groups of 4-5 students.
2. Provide each group with a practical projectile launch problem (e.g., a toy rocket launched from a platform).
3. Ask the groups to identify the coefficients a, b, and c from the given problem.
4. Guide each group to calculate the discriminant (Δ) of the equation.
5. With the value of Δ, the groups should use Bhaskara's formula to find the roots of the equation, which represent the launch and impact points of the projectile.
6. The groups should create a quick presentation (5 minutes) explaining their resolution process and the results found.

Objective: Apply Bhaskara's formula to solve a practical problem, developing teamwork skills and the presentation of results.

Duration: 35 - 40 minutes

Evaluation Exercises

1. Solve the equation 2x² - 4x - 6 = 0 using Bhaskara's formula. Identify the coefficients a, b, and c, calculate the discriminant, and find the roots.
2. An engineer is designing a bridge and needs to calculate the strength of a material. The equation he uses is x² + 6x + 9 = 0. Solve the equation and interpret the result.
3. In a financial market simulation, the equation modeling the behavior of a stock is 3x² - 12x + 9 = 0. Solve the equation and explain what the roots represent in this context.

Conclusion

Duration: 10 - 15 minutes

The purpose of this stage is to consolidate students' learning, ensuring they understand the practical application of quadratic equations and the importance of this knowledge for the job market. This moment of reflection and discussion allows students to internalize the concepts addressed and recognize the relevance of the skills developed during the class.

Discussion

Promote an interactive discussion about what was learned during the class. Ask students how they felt when applying Bhaskara's formula to practical problems and how this relates to potential situations they may encounter in the job market. Encourage them to share their reflections on the importance of understanding quadratic equations and how they can be used in various professional areas such as engineering, economics, and technology.

Summary

Summarize the main points covered in the class: identification of coefficients a, b, and c of a quadratic equation, calculation of the discriminant (Δ) and its interpretation, and application of Bhaskara's formula to find the roots of the equation. Reinforce the relevance of this knowledge for solving practical and situational problems.

Closing

Explain how the class connected theory with practice and applications. Highlight how students were able to see the application of quadratic equations in real contexts, such as the launch of projectiles and modeling financial behaviors. Conclude by mentioning the importance of mastering these mathematical concepts to increase employability and the ability to solve complex problems in everyday life.