Lesson Plan | Active Learning | Inequalities: Introduction

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 is designed to clearly establish what is expected of students by the end of the lesson. By defining precise goals, students can direct their study efforts and classroom participation more efficiently. This section is crucial to align the expectations of the teacher and the students, ensuring that everyone is focused on the same learning outcomes.

Main Objectives:

1. Empower students to solve basic first-degree inequalities using mathematical operations such as addition, subtraction, multiplication, and division, and interpret the results in the context of the signs of greater than, less than, greater than or equal to, and less than or equal to.

2. Develop logical reasoning skills and interpretation of mathematical problems, allowing students to apply the concept of inequalities in real and hypothetical situations.

Side Objectives:

1. Promote students' confidence in solving mathematical problems by encouraging active participation and group collaboration.

Introduction

Duration: (15 - 20 minutes)

The Introduction stage serves to engage students with content they have already studied at home, using problem situations to activate prior knowledge and contextualize the relevance of the topic. By presenting everyday situations that involve inequalities, students can perceive the direct applicability of the mathematical concept in their lives, increasing their interest and motivation to learn and apply the content in new contexts.

Problem-Based Situations

1. Consider that an electronics store is offering a 25% discount on all its products. If a customer has a budget of R$ 600.00, what are the maximum values they can spend on a product for the discount to be applied?

2. Imagine that a farmer needs to calculate how many bags of feed he can buy to feed his animals for a month. If he has a budget of R$ 1000.00 and each bag costs R$ 35.00, how many bags can he buy, considering that he cannot exceed his budget?

Contextualization

Inequalities are powerful mathematical tools that model everyday situations, such as purchasing decisions, financial planning, or even health issues. For example, by analyzing the calorie content in different foods, we can use inequalities to decide which choices are healthier within a daily calorie limit. This practical aspect helps to understand the importance of inequalities in daily life and motivates students to apply what they learn in real situations.

Development

Duration: (70 - 75 minutes)

The Development section is designed to allow students to practically and contextually apply the knowledge acquired about inequalities. By working in groups to solve everyday problems that involve calculations and financial decisions, students not only reinforce their mathematical understanding but also develop collaboration, critical thinking, and problem-solving skills. This active and participatory approach aims to consolidate learning and prepare students to apply mathematical concepts in various real-life situations.

Activity Suggestions

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

Activity 1 - Discount Challenge

> Duration: (60 - 70 minutes)

- Objective: Apply the concept of inequalities to solve practical problems of discount calculations, developing teamwork skills and mathematical reasoning.

- Description: Students will be divided into groups of up to 5 members to solve problems involving discount calculations applied to products in a store. Each group will receive a list of products with original prices and discount percentages, and they will need to calculate the new price after the discount, using inequalities to ensure that the price does not exceed a pre-established budget.

- Instructions:

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

• Distribute to each group a list of products with their original prices and the applied discount percentages.

• Ask the students to calculate the new prices after the discounts and to use inequalities to ensure that the final price does not exceed a fictional budget of R$ 1000.00.

• Each group will present their answers and the resolution process to the class.

Activity 2 - Champion's Budget

> Duration: (60 - 70 minutes)

- Objective: Use inequalities to solve a resource optimization problem, promoting critical thinking and practical application of mathematical concepts.

- Description: In this activity, students will be challenged to help an athlete manage their budget to buy sports equipment. They will receive a list of sports items with prices and a limited budget, and they must determine how many and which items the athlete can buy without exceeding their budget, using inequalities to model the possibilities.

- Instructions:

• Organize students into groups of no more than 5 participants.

• Provide each group with a list of sports items with varied prices and a budget of R$ 500.00.

• Students must use inequalities to determine how many of each item the athlete can buy, ensuring that the total spent does not exceed the budget.

• Each group presents their solutions and the resolution process to the class.

Activity 3 - The Balance Party

> Duration: (60 - 70 minutes)

- Objective: Develop financial planning skills and apply inequalities in decision-making situations, stimulating creativity and collaboration among students.

- Description: Students, working in groups, will plan a birthday party, considering the budget for decorations, food, and entertainment. They will receive a total amount available and prices for different services and products, and they must find the best combination that does not exceed the budget, using inequalities to model the restrictions.

- Instructions:

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

• Give each group a budget of R$ 800.00 and a list of services (decorations, food, entertainment) with different prices.

• Students must use inequalities to determine the possible combinations of services that fit within the budget without exceeding it.

• Each group presents their party proposal and the resolution process to the class.

Feedback

Duration: (15 - 20 minutes)

The purpose of this feedback stage is to consolidate learning by allowing students to articulate and share their discoveries and challenges. This group discussion helps reinforce understanding of mathematical concepts through the exchange of experiences and exposure to different problem-solving approaches. Additionally, this stage serves to assess students' understanding and ensure that the learning objectives have been achieved.

Group Discussion

To begin the group discussion, the teacher should gather all students in a large circle and introduce the topic: 'Today, each group had the opportunity to solve problems involving inequalities for financial decision-making. Let's share what we learned and discuss how inequalities helped us solve these challenges and reach practical solutions.' The teacher can also encourage students to reflect on the challenges encountered and the strategies used to overcome them.

Key Questions

1. What were the main challenges you faced in applying inequalities to solve the proposed problems?

2. How did inequalities help in making efficient decisions in situations of limited financial resources?

3. Is there any everyday situation where you imagine applying what you learned today about inequalities?

Conclusion

Duration: (5 - 10 minutes)

The purpose of the Conclusion stage is to consolidate learning by summarizing the main points covered during the lesson and reinforcing the applicability of mathematical concepts in everyday life. This final reflection helps students visualize the importance of what was learned and recognize how mathematics can be useful in solving real problems, motivating them to continue exploring and applying these concepts outside of the classroom.

Summary

In today's lesson, students explored the concept of inequalities, learning to solve problems involving mathematical inequalities. They applied these concepts in practical situations, such as discount calculations, financial planning, and purchase decisions, using inequalities to ensure that the solutions fit within previously established limits.

Theory Connection

Today's lesson served as a bridge between the mathematical theory of inequalities and its practical application. Students could see how mathematical concepts are essential for solving everyday problems, such as budgeting or comparing purchase options, highlighting the relevance of mathematics in their lives.

Closing

Understanding and applying inequalities is crucial in daily life, as it allows for informed decisions based on limits and conditions. This knowledge helps develop logical and mathematical reasoning skills, essential for problem-solving in various areas, from personal finance to science and technology.