Lesson Plan | Technical Methodology | Inverse Relationships of Operations

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage is to ensure that students clearly understand the relationship between inverse operations, such as subtraction and addition, and division and multiplication. This is fundamental not only for academic progress in mathematics but also for practical skills that will be useful in the job market, such as logical thinking and problem-solving. Through practical and collaborative activities, students will be able to apply these concepts effectively and develop relevant skills for the future.

Main Objectives

1. Identify that subtraction is the inverse operation of addition.

2. Recognize that division is the inverse operation of multiplication.

3. Use the concept of inverse operations to solve simple mathematical problems.

Side Objectives

1. Develop critical thinking and problem-solving skills.
2. Encourage collaboration and communication in group practical activities.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage is to ensure that students clearly understand the relationship between inverse operations, such as subtraction and addition, and division and multiplication. This is fundamental not only for academic progress in mathematics but also for practical skills that will be useful in the job market, such as logical thinking and problem-solving. Through practical and collaborative activities, students will be able to apply these concepts effectively and develop relevant skills for the future.

Contextualization

Imagine you are in a toy store with a fixed amount of money to spend. If you buy an expensive toy, you will have less money for other toys. But if you return that toy, you will get your money back to buy other items. This money exchange is a simple example of inverse operations in mathematics, where one action can be reversed by another.

Curiosities and Market Connection

Interesting curiosity: ATMs use inverse operations to check your account balance after a deposit or withdrawal. In the job market, especially in areas like accounting and engineering, understanding inverse operations is fundamental. For example, engineers use these concepts to solve complex equations when creating models that predict the behavior of structures and systems.

Initial Activity

To start the lesson, show a short 2-minute video that playfully explains the concept of inverse operations. Then, ask the following provoking question to the students: 'If you have 10 apples and give 3 to a friend, how many apples would you need to get back to have 10 apples again?'

Development

Duration: (50 - 60 minutes)

The purpose of this stage is to ensure that students can apply the concepts of inverse operations in practical situations and collaboratively solve mathematical problems. Through practical activities and fixation exercises, students will develop critical thinking, problem-solving, and teamwork skills, which are essential both in the academic context and in the job market.

Covered Topics

1. Inverse operations: addition and subtraction
2. Inverse operations: multiplication and division
3. Application of inverse operations in problem-solving

Reflections on the Theme

Guide students to reflect on how many everyday situations involve inverse operations. For example, when saving and spending money, assembling and disassembling puzzles, or tying and untying knots. Ask how difficult it would be to perform these activities if we did not know how to reverse an action.

Mini Challenge

Inverse Operations Challenge

Students will be divided into small groups to solve a mathematical challenge that involves building an 'inverse operations machine' using simple materials. This practical activity will help reinforce the concepts of addition, subtraction, multiplication, and division as inverse operations.

Instructions

1. Divide the students into groups of 3 to 4.
2. Provide each group with materials such as paper, pens, rulers, and numbered tokens.
3. Each group must create a 'machine' by drawing on a poster board how the inverse operations work.
4. For example, if a group chooses the operation of addition and subtraction, they could draw how 7 + 3 = 10 and 10 - 3 = 7.
5. The groups should present their machines to the class, explaining how the inverse operations work.
6. Encourage students to be creative and use colors and drawings to enhance understanding.

Objective: Reinforce understanding of inverse operations in a practical and collaborative way.

Duration: (25 - 30 minutes)

Evaluation Exercises

1. Solve the following problems using inverse operations: If you have 15 candies and give 5 to a friend, how many candies do you have? If you want to have the 15 candies back, how many do you need to get back? Divide 20 by 4. What is the inverse operation of this division and what would the result be?
2. Group problems: A group of friends has 24 stickers and decides to divide them equally among 6 friends. How many stickers does each friend receive? And if each friend decides to return their stickers, how many stickers would the group have in total again?
3. Explain how the inverse operation helps to solve the following problem: João had 12 stickers, he lost some and had 7 left. How many stickers did he lose?

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to consolidate students' learning, ensuring that they understand the relevance of inverse operations both in the academic context and in practical job market situations. Through recapitulation and discussion, students have the opportunity to reflect on what they learned and how to apply this knowledge in various situations.

Discussion

Facilitate an open discussion with the students about how the concept of inverse operations was applied in the practical activities, such as the 'inverse operations machine,' and in the fixation exercises. Encourage students to share their reflections on how inverse operations appear in everyday situations and in the job market, such as in financial transactions and technical problem-solving.

Summary

Recap the main points of the lesson, highlighting that subtraction is the inverse operation of addition and division is the inverse operation of multiplication. Reinforce how these concepts were applied in practical activities and proposed challenges.

Closing

Explain that understanding inverse operations is not only fundamental for mathematics but also for practical everyday situations and various professions. Encourage students to continue observing and applying these concepts in their daily routines and future studies.