Lesson Plan | Active Methodology | First Degree Equations

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)

This stage of the lesson plan aims to set clear learning objectives, outlining what students should achieve by the end of the lesson. By defining these objectives, the teacher guides students' focus and ensures that all activities align with reaching these specific goals.

Objective Utama:

1. Empower students to tackle real-world problems involving first-degree polynomial equations, using the format ax + b = c, while applying the principles of equality.

2. Develop skills for analyzing and interpreting practical situations, such as the scenario of a taxi fare, and translating them into equations for resolution.

Objective Tambahan:

1. Foster critical thinking and curiosity among students by connecting mathematical concepts to everyday experiences.

Introduction

Duration: (15 - 20 minutes)

This stage seeks to activate students' prior knowledge regarding first-degree equations through problem scenarios that encourage critical thinking. Moreover, contextualizing the content shows its relevance and practical impact, paving the way for a more engaging and meaningful learning experience.

Problem-Based Situation

1. Imagine you're planning a road trip and need to figure out the total cost of gas based on the distance you'll drive. The price of gas is fixed per litre, and you know how many litres your car uses per kilometer. How would you set up a first-degree equation to solve this?

2. Think about organizing a birthday party where you need to rent tables and chairs. The rental company charges a flat fee plus a per-item rental fee. How can you apply a first-degree equation to determine the total cost based on the number of tables and chairs you want to rent?

Contextualization

First-degree equations are commonly used in daily life, especially for calculating costs, distances, or times. For instance, they can help you figure out product prices by quantity or adjust work schedules based on a set rate. Additionally, grasping these equations allows students to interpret and solve real-world challenges, such as personal financial planning and event organization.

Development

Duration: (75 - 85 minutes)

The Development phase provides students the opportunity to actively and interactively apply the concepts of first-degree equations they have previously studied. Through engaging and contextualized activities, they will explore the real-world applications of these equations, enhancing problem-solving skills, critical thinking, teamwork, and communication. This method not only bolsters learning but also makes the content more relatable and impactful for students, increasing their retention and understanding.

Activity Suggestions

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

Activity 1 - The Mystery of the Missing Prices

> Duration: (60 - 70 minutes)

- Objective: Solve a practical problem to find the unit prices of products based on sales data by utilizing concepts of first-degree equations.

- Description: Students face a mystery involving the school store, where the prices of several items have vanished. They receive a list of products with quantities sold and total sales without the unit prices. Their task is to formulate first-degree equations based on the data to uncover the missing prices.

- Instructions:

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

• Hand out the product list along with quantities sold and total sales.

• Ask each group to create a system of linear equations to represent the situation, using x for the price of each item.

• Guide students to solve the equations and find the unit prices.

• Groups must then calculate and present the missing prices to the class.

Activity 2 - Household Budget Project

> Duration: (60 - 70 minutes)

- Objective: Apply first-degree equation concepts to tackle real-world challenges in family budgeting, enhancing financial planning skills.

- Description: In this task, students plan a family's monthly budget, including fixed expenses like rent and internet, along with variable expenses such as food and transport. They are given a hypothetical salary and must allocate their funds without exceeding their total budget, using first-degree equations to manage their spending.

- Instructions:

• Form groups of up to 5 students, each representing a family.

• Provide them with a monthly salary and a list of fixed and variable costs.

• Students must create equations to represent their total monthly spending, where x will denote the amount of variable expenses.

• Guide the groups to solve the equations to determine how much they can spend on variable costs.

• Each group presents a detailed budget plan, explaining their choices.

Activity 3 - Mathematical Taxi Race

> Duration: (60 - 70 minutes)

- Objective: Comprehend and apply first-degree equations within a variable cost context, fostering teamwork and healthy competition.

- Description: Students will simulate a taxi ride, where the trip's cost includes a set starting fee and a charge per kilometer traveled. They will calculate trip costs over various distances by modeling the fare with first-degree equations. The activity also features a friendly competition to see which group can achieve the lowest fare.

- Instructions:

• Split the class into groups of up to 5 students, each with a distinct starting point and destination.

• Assign a flat rate and a charge per kilometer to each group.

• Students will then model a first-degree equation to calculate the taxi fare based on their distance.

• Kick off the race and have each group compute the cost of their trip.

• The group that reaches their destination with the lowest cost without going over budget wins.

Feedback

Duration: (15 - 20 minutes)

This stage aims to solidify students' learning, allowing them to reflect on their experiences and share insights with their peers. Group discussions help identify misunderstandings and clarify remaining questions, while fostering communication and reasoning skills. This exchange of ideas enriches students' grasp of the application of first-degree equations in various scenarios, ensuring that the knowledge is absorbed more effectively.

Group Discussion

To kick off the group discussion, the teacher should prompt each group to share their findings and any challenges they encountered during problem-solving. Encourage students to discuss not just the answers but the thought processes behind them. The teacher can initiate the session with a general question like 'What were the main hurdles your group faced while applying first-degree equations to these problems?' giving each group the chance to reflect and contribute.

Key Questions

1. How did you utilize the properties of equality when solving your first-degree equations?

2. Was there a particular step in the process that was especially challenging? How did your group tackle that?

3. In what ways could first-degree equations be helpful in real-life situations we didn’t pinpoint today?

Conclusion

Duration: (5 - 10 minutes)

The purpose of the Conclusion stage is to ensure that students have a clear and consolidated understanding of the concepts covered in the lesson, recognizing both the practical and theoretical significance of first-degree equations. This stage serves to reinforce learning, clear up any lingering doubts, and ensure that students can apply the knowledge gained in contexts beyond the classroom.

Summary

In the lesson’s conclusion, the teacher should wrap up by summarizing the key concepts covered, such as solving first-degree equations and their practical uses in real life. It’s vital that students can recall and solidify their learning, ensuring all discussed topics are understood and retained.

Theory Connection

Throughout the lesson, we established connections between the mathematical theory of first-degree equations and practical applications through activities simulating real-life scenarios, like calculating product costs, planning family budgets, and simulating taxi rides. This method not only facilitated comprehension of the material but also showcased the significance of mathematics in everyday situations.

Closing

To close, it’s important to underscore the relevance of first-degree equations in our daily lives. Mastering these equations is essential for simple tasks like budgeting for purchases or computing expenses, as well as more complex activities such as managing budgets and pricing in business. Understanding and applying these concepts prepares students to tackle real challenges across various aspects of their lives.