Lesson Plan | Technical Methodology | Fractions: Multiplication and Division

Objectives

Duration: 10 to 15 minutes

The purpose of this stage is to provide a solid understanding of the concepts of multiplication and division of fractions, essential for solving more complex mathematical problems. By connecting these concepts with practical applications and the job market, students develop relevant skills that can be applied in real contexts, promoting meaningful and lasting learning.

Main Objectives

1. Understand the basic concepts of multiplication and division of fractions.

2. Apply techniques of multiplication and division of fractions in practical problems.

Side Objectives

1. Develop problem-solving skills through mini practical challenges.

Introduction

Duration: 10 to 15 minutes

The purpose of this stage is to contextualize the theme, connect the content with real situations and the job market, and engage students' interest. This creates a solid and motivating foundation for learning operations with fractions, demonstrating the relevance and applicability of this knowledge.

Contextualization

Fractions are present in our daily lives in various forms, such as when dividing a pizza into equal parts or measuring ingredients for a recipe. Understanding how to multiply and divide fractions is essential for dealing with real situations that involve proportions and precise divisions. This lesson will help students develop these fundamental skills.

Curiosities and Market Connection

Curiosity: Did you know that multiplying and dividing fractions is fundamental in civil engineering? Professionals in this field frequently use these operations to calculate material proportions in construction. In the job market, fractions are essential in areas such as culinary arts, where chefs need to adjust recipes, and in finance, where analysts calculate returns and distribution of investments.

Initial Activity

To spark students' interest, start the lesson with the following provocative question: 'If you had to evenly divide 3/4 of a pizza among 3 friends, how much would each receive?' Then, show a short video (2 to 3 minutes) that showcases practical applications of fractions in different professions.

Development

Duration: 60 to 65 minutes

The purpose of this stage is to ensure that students understand and apply the operations of multiplication and division of fractions through practical activities and fixation exercises. This promotes active and meaningful learning, connecting mathematical content to daily life and the job market.

Covered Topics

1. Multiplication of fractions
2. Division of fractions
3. Practical applications of fraction operations

Reflections on the Theme

Guide students to reflect on how fractions are used in various professions, such as in culinary arts, engineering, and finance. Ask: 'How can the ability to multiply and divide fractions influence precision and efficiency in different professional areas?' Encourage them to think of everyday situations where these operations are needed.

Mini Challenge

Building a Recipe with Fractions

In this activity, students will work in groups to adjust a recipe using fractions. They will need to multiply and divide fractions to adjust the amounts of ingredients.

Instructions

1. Divide the class into groups of 3 to 4 students.
2. Distribute a simple recipe (e.g., cake) and indicate that they need to adjust the amounts to serve a different number of people (e.g., the original recipe serves 4 people, but they need to adjust it for 10 people).
3. Instruct each group to multiply the fractions of the ingredients by the corresponding fraction for the increase or decrease in servings.
4. Then, ask each group to present how they adjusted the recipe and what multiplication and division operations were performed.
5. During the presentation, ask questions to ensure that all group members understand the process.

Objective: Apply the operations of multiplication and division of fractions in a practical situation, promoting group collaboration and understanding of the real applications of these operations.

Duration: 35 to 40 minutes

Evaluation Exercises

1. Solve the following multiplication operations of fractions: ( \frac{2}{3} \times \frac{3}{4} = \frac{1}{2} ), ( \frac{5}{6} \times \frac{2}{5} = \frac{1}{3} ), ( \frac{7}{8} \times \frac{1}{2} = \frac{7}{16} )
2. Solve the following division operations of fractions: ( \frac{3}{4} \div \frac{2}{3} = \frac{9}{8} ), ( \frac{5}{6} \div \frac{1}{2} = \frac{5}{3} ), ( \frac{7}{8} \div \frac{1}{4} = \frac{7}{2} )
3. Solve the problem: You are building a model of a building at a 1:20 scale. If the real height of the building is 60 meters, what will be the height of the model? (Answer: 3 meters)

Conclusion

Duration: 10 to 15 minutes

The purpose of this stage is to consolidate the knowledge acquired by students during the lesson, reinforcing the connection between theory, practice, and application. Additionally, the conclusion serves to reflect on the importance of operations with fractions in daily life and the job market, ensuring that students comprehend the relevance of the content studied.

Discussion

Promote an open discussion with students about how fractions were used in different activities during the lesson. Ask them how they felt when adjusting the recipe and what challenges they faced during the calculations. Encourage them to share everyday situations where they can apply multiplication and division of fractions. Reinforce the importance of understanding these operations for precision and efficiency in various professions, such as culinary arts, engineering, and finance.

Summary

Recap the main contents covered during the lesson: the multiplication and division of fractions, the practical application of these concepts in adjusting recipes, and the importance of fractions in different professional contexts. Reinforce how each activity contributed to the understanding of these mathematical concepts.

Closing

Explain how the lesson connected mathematical theory with practice through interactive activities and discussions about real applications. Emphasize the relevance of mastering operations with fractions to solve everyday problems and for various careers. Highlight that the knowledge gained today is a valuable tool they will carry with them for a lifetime.