Lesson Plan | Active Learning | First Degree Function: Inputs and Outputs

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5 - 10 minutes)

The objectives stage aims to clearly establish what is expected for students to learn and master by the end of the lesson. By defining focused objectives, the teacher provides clear direction for the students, facilitating understanding of expectations and maximizing the efficiency of learning time in the classroom. This stage also serves to align subsequent activities with learning objectives, ensuring a cohesive and targeted educational experience.

Main Objectives:

1. Ensure that students can recognize and define linear functions.

2. Enable students to identify inputs (independent variables) and outputs (dependent variables) in linear functions.

Side Objectives:

1. Develop skills for analyzing and interpreting graphs that represent linear functions.
2. Stimulate logical and mathematical reasoning through solving practical problems involving linear functions.

Introduction

Duration: (15 - 20 minutes)

The introduction phase aims to engage students by using problem situations that help them connect the studied concepts with practical applications, preparing them to deepen their understanding during the lesson. Additionally, contextualization illustrates the relevance of the topic in the real world, increasing student interest and motivation.

Problem-Based Situations

1. Imagine you are a merchant who needs to calculate daily sales totals based on the quantity of products sold and the fixed price of each one. How would you use a linear function to model this situation?

2. Think of a taxi company that charges an initial fare plus a fixed amount per kilometer traveled. How could a linear function be used to calculate the total cost of a trip based on the kilometers traveled?

Contextualization

Linear functions are deeply rooted in everyday operations, from calculating costs in business to forecasting expenses in personal and professional projects. Understanding these functions is not just a mathematical skill but an essential tool for making informed and efficient decisions in various aspects of daily life.

Development

Duration: (70 - 75 minutes)

The development stage aims to consolidate students' knowledge of linear functions through practical activities that simulate real situations. These activities are designed to be challenging and interactive, encouraging students to creatively and effectively apply the concepts learned. Choosing only one activity allows for significant depth, ensuring that students can fully explore the mathematical concepts involved and develop problem-solving, teamwork, and presentation skills.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - Merchant for a Day

> Duration: (60 - 70 minutes)

- Objective: Apply knowledge of linear functions to solve real business problems and understand how variations in prices and quantities affect final profit.

- Description: In this activity, students will take on the role of merchants who need to calculate daily profit based on the quantity of products sold and the fixed price of each one. Each group will receive cards with different products and prices, as well as a hypothetical sales demand for each product.

- Instructions:

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

• Distribute the product cards and sales demands.

• Students should apply the linear function to calculate the total sales.

• Each group should present a brief report on sales and profits at the end.

• Encourage students to discuss strategies used to maximize profits by applying variations in product prices.

Activity 2 - Mathematical Taxi Drivers

> Duration: (60 - 70 minutes)

- Objective: Use linear functions to calculate costs in a taxi service context, developing skills in mathematical application in practical business situations.

- Description: Students will be divided into groups, and each group will represent a taxi company. They must calculate the total cost of various trips, considering an initial fare and a fixed amount per kilometer traveled, using linear functions.

- Instructions:

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

• Provide each group with information about fares and travel distances.

• Groups must use the linear function to calculate the cost of each trip.

• They should also consider scenarios with discounts or different fares for long trips.

• Each group will present a fare table and cost-benefit ratio for customers.

Activity 3 - The Mathematics of Shows

> Duration: (60 - 70 minutes)

- Objective: Explore the use of linear functions in financial planning for events, empowering students to perform calculations of costs, revenue, and profit.

- Description: Students, in groups, will assume the role of event promoters who need to calculate the costs and revenue of shows based on the number of tickets sold and the price of tickets, using linear functions.

- Instructions:

• Divide students into groups of up to 5.

• Provide each group with information about fixed organization costs and variable ticket prices.

• Groups must calculate the break-even point and the expected profit with different quantities of tickets sold.

• Students will create graphs to visually represent their findings.

• At the end, each group will present the financial viability of the proposed event.

Feedback

Duration: (10 - 15 minutes)

This stage of the lesson plan aims to provide students with the opportunity to reflect on their acquired learning and consolidate their knowledge through the exchange of experiences. Group discussion allows students to articulate their understandings and questions, which is crucial for deepening their understanding of the topic and for the practical application of knowledge in future situations.

Group Discussion

At the end of the activities, gather all students for a group discussion. Start the discussion with a brief introduction about the importance of applying mathematics to solve real-world problems. Encourage each group to share their strategies, challenges faced, and solutions found during the activities. Ask how they would apply what they learned in other practical situations outside the classroom.

Key Questions

1. What were the main challenges in applying linear functions in the proposed activities?

2. How did altering variables in the function affect the final results in your activities?

3. In what ways could you use the knowledge about linear functions to solve other practical problems?

Conclusion

Duration: (5 - 10 minutes)

The conclusion stage serves to solidify students' understanding by synthesizing the key concepts discussed and the activities carried out. It is an opportunity for the teacher to reinforce the connection between theory and practice, as well as to highlight the relevance of mathematical concepts in daily life. This stage is crucial to ensure that students leave the lesson with a clear understanding of the learning objectives and the ability to apply their acquired knowledge in new contexts.

Summary

To conclude the lesson, recap the main points covered about linear functions, emphasizing how each activity helped illustrate the concept of inputs and outputs. Review the practical applications discussed, such as calculating costs in different business and personal scenarios, and the impact of these concepts on solving everyday problems.

Theory Connection

Explain how the practical activities performed in class served to connect mathematical theory with real applications, highlighting the importance of the linear function in modeling practical situations. Show how this approach helps students gain a better understanding of mathematical concepts by seeing their direct application.

Closing

End the lesson by highlighting the relevance of linear functions in daily life, showing how this knowledge is essential for making informed decisions in various contexts, from personal finance to business strategies. Emphasize that mathematics is a powerful tool that, when well understood, can open new perspectives and opportunities.