Lesson Plan | Active Methodology | Quadratic Equation: Bhaskara

Premises: This Active Lesson Plan assumes: a 100-minute class duration, prior student study both with the Book and the beginning of Project development, and that only one activity (among the three suggested) will be chosen to be carried out during the class, as each activity is designed to take up a large part of the available time.

Objective

Duration: (5 - 10 minutes)

The phase of setting objectives is vital to direct student focus and ensure that learning expectations are clear. This section articulates goals in a straightforward manner so students know what's expected of them by the lesson's end. This clarity maximizes classroom time, allowing both teachers and students to concentrate on the established goals and apply newly acquired knowledge both practically and theoretically.

Objective Utama:

1. Enable students to solve quadratic equations using the Bhaskara formula to find their roots.

2. Encourage students to apply quadratic equations in both practical and theoretical contexts, reinforcing their understanding of the method and its usefulness.

Objective Tambahan:

1. Foster logical and critical reasoning skills in the manipulation of complex mathematical formulas.
2. Promote collaboration and communication among students during practical activities.

Introduction

Duration: (20 - 25 minutes)

The introduction phase aims to engage students by revisiting concepts learned at home while highlighting the practical importance of the quadratic equation and the Bhaskara formula. Presenting problem scenarios encourages critical thinking and the practical application of their knowledge, laying the groundwork for classroom activities. This contextualization, enriched with real examples and historical insights, boosts interest and highlights the topic's relevance.

Problem-Based Situation

1. Think of a scenario where a farmer wants to split his field into two sections: one for crops and the other for livestock. The total area is 1200 square meters. He's decided the crop area will be a rectangle measuring 30 meters long, while the livestock area will be a square. How should he divide the field to maximize the livestock area?

2. Consider a party rental company trying to figure out how to price a wedding hall. The rental consists of a fixed fee and a variable cost per square meter. The fixed fee is $2000, and the cost per square meter is $20. If the hall is square-shaped, how can the company use the Bhaskara formula to calculate the total rental price based on different hall sizes?

Contextualization

The Bhaskara formula isn't just a mathematical concept; it has real-world applications in fields like engineering, physics, and economics. Calculating the roots of a quadratic equation can help identify critical points in functions, essential for optimizations in engineering projects. Additionally, sharing interesting facts about Bhaskara, a 12th-century Indian mathematician, can help students appreciate the significance and rich history of mathematics.

Development

Duration: (70 - 75 minutes)

The development stage is set up for students to practically and contextually apply the concepts they've studied about quadratic equations and the Bhaskara formula. Through engaging and challenging activities—like solving mathematical puzzles or participating in 'mathematical investigations'—students will work in groups to tackle problems that mimic real-life situations, requiring not just mathematical knowledge but also communication, collaboration, and critical thinking skills. This approach is intended to solidify their learning and make mathematics more appealing and relatable.

Activity Suggestions

It is recommended that only one of the suggested activities be carried out

Activity 1 - Square Roots Challenge

> Duration: (60 - 70 minutes)

- Objective: Practice using the Bhaskara formula in various situations while developing teamwork and communication skills.

- Description: In this activity, students will tackle a series of quadratic equations using the Bhaskara formula. Each group will receive a selection of equations of varying complexity and will aim to solve as many as possible within a set time. The equations will relate to diverse contexts, such as optimization challenges, geometry, and everyday scenarios.

- Instructions:

• Form groups with a maximum of 5 students.

• Distribute a set of quadratic equations to each group.

• Set a 60-minute time limit to solve the equations.

• Have each group present their solutions and the methods used.

• Conclude by discussing the different approaches and solutions within the class.

Activity 2 - The Mystery of the Missing Coordinates

> Duration: (60 - 70 minutes)

- Objective: Enhance problem-solving skills involving quadratic equations and reinforce understanding of coordinates within the Cartesian plane.

- Description: Students, grouped together, will receive a 'map' with a series of coordinates that form a geometric figure. The challenge is to identify the missing coordinates that will complete a perfect square. To do this, they will solve quadratic equations and apply basic geometry principles.

- Instructions:

• Divide the class into groups of up to 5 students.

• Provide each group with a 'map' displaying partial coordinates of a square.

• Students should utilize the Bhaskara formula to determine the missing coordinates.

• Set a 60-minute deadline to solve the mystery.

• Each group will present their findings and the resolution process.

Activity 3 - Mathematical Investigation: The Case of the Missing Coefficients

> Duration: (60 - 70 minutes)

- Objective: Enhance the application of the Bhaskara formula in problem-solving contexts while encouraging critical thinking and collaboration.

- Description: In this 'math detective' scenario, students will work in groups to solve a mystery involving stolen coefficients from a quadratic equation. They will need to use clues and context to uncover the missing coefficients and solve the equation to find the 'culprit.'

- Instructions:

• Organize students into groups of up to 5.

• Distribute 'clues' containing partial details about the quadratic equation.

• Have students apply the Bhaskara formula to identify the unknown coefficients.

• Establish a 60-minute timeframe to resolve the case.

• Each group will present their solution along with their reasoning.

Feedback

Duration: (15 - 20 minutes)

The feedback stage is crucial for solidifying students' learning, prompting them to reflect on what they've absorbed and share their discoveries with peers. This discussion reinforces understanding of mathematical concepts, identifies potential areas of difficulty, and values the collaborative efforts. Moreover, the key questions guide students to reflect on the practical implications of their learning, facilitating the transfer of knowledge to new contexts.

Group Discussion

Kick off the group discussion by inviting each team to share their experiences and findings. Use a board or projection to allow each group to visually present their solutions and the processes they used. Encourage students to articulate the reasoning behind their choices and methods. This discussion is an opportunity for everyone to learn from diverse approaches and exchange ideas on the challenges faced.

Key Questions

1. What were the key challenges faced when solving quadratic equations with the Bhaskara formula?

2. In what ways can the application of quadratic equations be beneficial in everyday situations?

3. Was there a particular teamwork strategy or method that stood out during the activity?

Conclusion

Duration: (10 - 15 minutes)

The conclusion phase is aimed at consolidating students’ learning, ensuring they've understood the main concepts of the lesson. Recapping the central points aids in reinforcing memory and comprehension, while exploring the connection between theory and practice and the relevance of the content to real-life situations promotes the application of knowledge across various contexts. This moment of reflection and closure is critical for students to appreciate the usefulness of what they've learned and the importance of continuing to explore mathematics in their everyday lives.

Summary

To wrap up, the teacher should summarize the key points covered, including the Bhaskara formula, the process of solving quadratic equations, and the practical applications discussed, such as optimization and geometry problems. This recap reinforces learning and ensures students understand the fundamental concepts.

Theory Connection

Throughout the lesson, the connection between theory and practice was established through activities that mimic real-world situations, such as the 'Square Roots Challenge' and the 'Mathematical Investigation.' These exercises enabled direct application of the theory learned at home, while also emphasizing the relevance of mathematics in daily life, enhancing the perceived value of the material covered.

Closing

Studying quadratic equations and the Bhaskara formula is important not just academically; it plays a significant role in various professional fields and everyday problem-solving. Mastering these concepts empowers students not only to progress in mathematics but also to develop analytical and problem-solving skills that are essential in many practical scenarios.