Lesson Plan | Traditional Methodology | Unequal Partition Problems

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to prepare students to understand the concept of unequal sharing, providing a solid foundation for solving mathematical problems that involve the division of quantities in a disproportionate way. This step helps ensure that students are ready to approach and understand the subsequent examples and exercises that will be presented during the lesson.

Main Objectives

1. Understand the notion of unequal sharing and its application in practical problems.

2. Learn to solve division problems involving quantities in unequal parts, specifically where one part is double the other.

3. Develop skills to identify and apply the correct strategy in problems of unequal sharing.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to prepare students to understand the concept of unequal sharing, providing a solid foundation for solving mathematical problems that involve the division of quantities in a disproportionate way. This step helps ensure that students are ready to approach and understand the subsequent examples and exercises that will be presented during the lesson.

Context

Start the lesson by explaining to students that in many everyday situations, we need to divide things among people in an unequal manner. For example, when an older sibling receives more allowance than the younger sibling or when a larger piece of cake is given to the birthday person. These situations can be represented mathematically and help to understand how to deal with quantities fairly but unequally.

Curiosities

Did you know that in nature, unequal sharing is common? For example, in a bee colony, the queen bee receives a much larger amount of special food (royal jelly) than the worker bees, so she can grow and develop more than the other bees.

Development

Duration: (30 - 40 minutes)

The purpose of this stage of the lesson plan is to provide students with a practical and detailed understanding of how to solve problems of unequal sharing. By addressing specific topics and solving practical examples, students will be able to apply the knowledge acquired in similar situations, strengthening their ability to divide quantities in a disproportionate way.

Covered Topics

1. Introduction to Unequal Sharing: Explain the concept of unequal sharing, highlighting that in some situations it is necessary to divide a quantity into parts that are not equal. Exemplify with everyday situations where this occurs, such as the division of inheritances or the distribution of tasks. 2. Division into Unequal Parts: Detail how to divide a total quantity into two unequal parts, specifically when one part is double the other. Use a step-by-step approach, showing how to define the parts and check the correct division. 3. Practical Example: Present a practical example, such as dividing 30 stickers into two parts, where one part is double the other. Show the detailed calculation: 30 = x + 2x, resulting in x = 10 and 2x = 20, that is, 10 and 20 stickers, respectively.

Classroom Questions

1. If you have 24 candies and need to divide them into two unequal parts, so that one part is double the other, how many candies will there be in each part? 2. A teacher has 45 pencils and wants to divide them between two students so that one receives double the pencils of the other. How many pencils will each student receive? 3. John and Mary have a total of 36 toys. If John has twice as many toys as Mary, how many toys does each one have?

Questions Discussion

Duration: (20 - 25 minutes)

The purpose of this stage of the lesson plan is to review and consolidate students' understanding of unequal sharing, ensuring that they comprehend the methods and reasoning used to solve the presented problems. This stage also offers the opportunity to engage students in discussions, allowing them to share their approaches and reflections, which can further enrich collective learning.

Discussion

• Question 1: If you have 24 candies and need to divide them into two unequal parts, so that one part is double the other, how many candies will there be in each part?

To solve this question, start by defining the unequal parts. Let's call the smaller part 'x' and the larger part '2x'. We know that the sum of both parts is 24 candies. So we can write the equation:

x + 2x = 24

Simplifying, we have:

3x = 24

Dividing both sides of the equation by 3, we get:

x = 8

Therefore, the smaller part is 8 candies and the larger part is 16 candies (2x8).

• Question 2: A teacher has 45 pencils and wants to divide them between two students so that one receives double the pencils of the other. How many pencils will each student receive?

First, we define the unequal parts. We call the smaller part 'y' and the larger part '2y'. We know that the sum of both parts is 45 pencils. So the equation is:

y + 2y = 45

Simplifying, we have:

3y = 45

Dividing both sides of the equation by 3, we get:

y = 15

Thus, the smaller part is 15 pencils and the larger part is 30 pencils (2x15).

• Question 3: John and Mary have a total of 36 toys. If John has twice as many toys as Mary, how many toys does each one have?

We define the unequal parts. We call the number of toys Mary has 'z' and the number of toys John has '2z'. We know that the sum of both parts is 36 toys. So we write the following equation:

z + 2z = 36

Simplifying, we have:

3z = 36

Dividing both sides of the equation by 3, we get:

z = 12

Therefore, Mary has 12 toys and John has 24 toys (2x12).

Student Engagement

1. How did you arrive at the solutions to the questions? Did anyone use a different method? 2. Why is it important to understand how to make an unequal sharing? 3. Can you think of other everyday situations where unequal sharing is necessary? 4. How can we verify if our solution is correct? 5. What difficulties did you encounter when solving these questions?

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to review and consolidate the knowledge acquired by students throughout the lesson, ensuring they understand the concepts and know how to apply them. Recapping the main points and discussing their relevance helps to reinforce the content and demonstrate the practical importance of what was learned.

Summary

• Concept of Unequal Sharing: It was explained that in many everyday situations it is necessary to divide quantities in an unequal way.
• Division into Unequal Parts: Details on how to divide a total quantity into two unequal parts, especially when one part is double the other.
• Practical Example: Division of 30 stickers into two parts where one is double the other, resulting in 10 and 20 stickers, respectively.
• Problem Solving: Practical problems were solved, such as dividing 24 candies, 45 pencils, and 36 toys into unequal parts, with each example detailed step by step.

The lesson connected the theory of unequal sharing with practice through concrete examples and practical problems, showing students how to apply formulas and methods to solve real situations of disproportionate division of quantities.

Understanding unequal sharing is important in everyday life, as we often need to divide things fairly but unequally. This occurs in situations such as the division of inheritances, distribution of tasks, and even in nature, as exemplified by the bees. Knowing how to solve these problems helps to better deal with practical situations and develop fundamental mathematical skills.