Objectives (5 - 7 minutes)

1. Understand and recognize the inverse relationship of mathematical operations of addition and subtraction, and multiplication and division.
2. Identify and correctly apply the inverse relationship of operations in everyday mathematical problems.
3. Demonstrate the ability to solve mathematical problems involving the inverse relationship of addition and subtraction, and multiplication and division.

These objectives are fundamental to develop students' mathematical foundation in the early years of elementary school. Understanding the inverse relationship between mathematical operations is crucial for building knowledge and solving more complex problems later on. Through interactive activities and real-life examples, students will be encouraged to explore and apply these concepts in a meaningful way.

Introduction (10 - 12 minutes)

1. Review of Previous Content: The teacher starts the lesson by reviewing fundamental mathematical concepts that students have already learned, such as addition, subtraction, multiplication, and division. This can be done through direct questions to the students, such as "What is addition?" and "What is the result of the operation 5+3?".

2. Problem Situations: The teacher proposes two problem situations that students can easily relate to their everyday experiences.

   • First, the teacher can ask: "If you have 10 candies and give 3 to a friend, how many candies will you have left?"
   • Then, the teacher can ask: "If you have 10 dollars and want to buy 3 candies, how much money will you have left?"

3. Contextualization: The teacher explains that these problem situations are examples of how mathematical operations relate to each other. He explains that when we have to subtract 3 from 10, we are using the inverse operation of addition. Similarly, when we have to find out how many times one number fits into another, we are using the inverse operation of multiplication, division.

4. Capturing Students' Attention: The teacher proposes two mathematical curiosities that may spark students' interest in the subject:

   • First, he can mention that the idea of inverse operations was used by ancient Egyptian and Babylonian mathematicians to solve everyday problems, such as dividing lands or distributing food fairly.
   • Then, he can show that inverse operations are so important that they are used in many other areas beyond mathematics, such as computer programming and solving scientific problems.

5. Introduction to the Topic: The teacher introduces the topic of the lesson, explaining that they will learn more about inverse operations and how they are used to solve problems. He tells the students that they will see how addition and subtraction, and multiplication and division are operations that complement each other, and that understanding this will help them become better at mathematics. With this, the introduction of the lesson is concluded, and the students are prepared to deepen their learning about the inverse relationship of operations.

Development (20 - 25 minutes)

Here are three activity suggestions that the teacher can choose to implement in the classroom. Each activity is designed to help students understand the inverse relationship of operations in a playful and engaging way. The teacher can choose one of the activities or adapt all of them to meet the needs and skill level of their class.

1. Building the Math Tower:

   • The teacher divides the class into groups of 3 to 4 students. Each group receives a stack of colored cards numbered from 1 to 10 and a die.
   • The game starts with one student from each group rolling the die and picking the card corresponding to the rolled die face. For example, if the student rolls the die and gets the number 3, they must pick the card with the number 3 from the stack.
   • The student then has to think of an operation that, when applied to the card's number, results in a number that has already been removed from the stack. For example, if the card's number is 3 and the number 2 has already been removed from the stack, the student can do the subtraction 3 - 2.
   • If the operation is correct, the student removes the used card and the result of the operation from the stack. If it is incorrect, the card is returned to the stack, and the next student rolls the die.
   • The game continues until all cards are removed from the stack, or until no number can be obtained through the available operations.
   • The group that removes the most cards from the stack wins.

2. The Operations Magician:

   • The teacher writes various numbers and operations on pieces of paper and places them in a hat or box.
   • One student at a time picks a paper. If it is a number, they must say which inverse operations can be used to reach this number. If it is an operation, they must say what the inverse operation of it is.
   • If the student answers correctly, they earn a point. If they are wrong, the paper is returned to the hat or box, and the next student takes a turn.
   • The game continues until all papers have been picked. The student with the most points is the "Operations Magician".

3. Hidden Treasure Mathematical Problems:

   • The teacher hides several cards with mathematical problems around the classroom. Each card has a mathematical problem involving the inverse relationship of operations. For example: "A number multiplied by 5 equals 20. What is the number?"
   • The students, in groups, must search for the cards and solve the problems. The group that finds the highest number of correctly solved cards wins the game.

Remember that these are suggestions, and the teacher can adapt the activities according to the needs and profile of their class. The important thing is that the activities are playful, interactive, and challenging, so that students can truly understand the inverse relationship of operations and have fun learning Mathematics.

Return (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes):

   • After completing the activities, the teacher gathers all students in a large circle for a group discussion. Each group will have the opportunity to share their discoveries, solutions, and strategies used during the activities.
   • The teacher should encourage students to explain how they arrived at their answers, emphasizing the importance of using inverse operations correctly.
   • During the discussion, the teacher should ask questions that allow students to identify the inverse operations used in each problem and how they relate to the original operations.
   • The teacher can also ask students to demonstrate the inverse relationship of operations in practical examples, thus reinforcing what was learned during the lesson.

2. Connection to Theory (3 - 4 minutes):

   • After the group discussion, the teacher revisits the theoretical concepts presented at the beginning of the lesson and connects them to the solutions and strategies discussed by the students.
   • The teacher reinforces that addition and subtraction, as well as multiplication and division, are operations that complement each other. He also emphasizes the importance of using inverse operations to solve mathematical problems efficiently.
   • The teacher can use the examples discussed by the students to illustrate how theory applies to practice, making learning more meaningful and relevant for the students.

3. Final Reflection (2 - 4 minutes):

   • To conclude the lesson, the teacher suggests that students reflect silently for a minute on what they learned during the lesson. He can ask two simple questions to guide students' reflection: "What was easiest for you in today's lesson?" and "What was most challenging for you in today's lesson?".
   • After the reflection, the teacher gives the opportunity for some students to share their answers. He should validate both answers indicating ease and those indicating challenge, emphasizing that learning is a continuous process and that everyone is making progress, regardless of the difficulties encountered.
   • Finally, the teacher reinforces that practice is important to improve understanding and mastery of the inverse relationship of operations, and that they will have more opportunities to explore this concept in the upcoming lessons.

This return is essential to consolidate students' learning, allowing them to reflect on what they have learned, connect theory with practice, and identify any gaps in understanding that may exist. In addition, group discussion and individual reflection promote active student participation, critical thinking, and self-assessment - fundamental skills for effective and lasting learning.

Conclusion (5 - 7 minutes)

1. Lesson Summary (2 - 3 minutes):

   • The teacher starts the conclusion by recalling the main points covered during the lesson. He recaps the idea that addition and subtraction, as well as multiplication and division, are operations that complement each other.
   • He reinforces that to solve mathematical problems, it is necessary to use inverse operations correctly. For example, if we need to find out how many cards we have after removing some, we use the subtraction operation, which is the inverse of addition.

2. Connection between Theory and Practice (1 - 2 minutes):

   • Next, the teacher emphasizes how the lesson connected theory and practice. He reminds students that during the activities, they were able to see in practice how inverse operations work.
   • The teacher also highlights that the problem situations and games proposed in the lesson are examples of how mathematics can be fun and useful in everyday life.

3. Extra Materials (1 minute):

   • The teacher suggests some extra materials for students who wish to deepen their knowledge on the subject. This may include fun math books, educational apps, or websites with games and interactive activities.
   • Additionally, the teacher may suggest that students practice at home by solving everyday math problems involving the inverse relationship of operations. For example, they can try to solve a simple problem like "If we have 12 pencils and want to divide them equally among 4 friends, how many pencils will each receive?".

4. Importance of the Subject (1 minute):

   • Finally, the teacher highlights the importance of the subject for everyday life. He explains that the ability to understand and use inverse operations is essential for solving mathematical problems, but can also be useful in many other situations, such as task division, food distribution, or computer programming.
   • The teacher concludes the lesson by encouraging students to continue exploring mathematics in a fun and curious way, and reminding them that practice is key to improving their mathematical skills.

This conclusion helps solidify students' learning, reinforcing key concepts and the connection between theory and practice. Additionally, it provides suggestions for deepening knowledge and emphasizes the importance of the subject, motivating students to continue exploring mathematics beyond the classroom.