Objectives (5 minutes)

1. Introduce the concept of 'division remainder' to students, explaining that when we divide one number by another, we do not always get an exact division, and what is left after this division is called the remainder.
2. Teach students how to calculate the remainder of a division, using simple and understandable examples for their age group.
3. Present practical applications of the concept of division remainder, demonstrating how this mathematical skill is useful in everyday life.

Introduction (10 - 15 minutes)

1. Concept Review: The teacher starts the lesson by reminding students about the concept of division and its basic properties, such as dividing objects into equal parts and the idea that division is the inverse operation of multiplication. This can be done through questions and answers with the class and quick activities solving simple division problems.

2. Problem Situation 1: The teacher presents the first problem situation: 'Imagine we have 12 candies and want to divide them equally among 5 friends. Can we do that? Why?' The goal is for students to realize that, in this case, it is not possible to divide the candies equally, and that there is always some remainder.

3. Problem Situation 2: Next, the teacher presents the second problem situation: 'Now, let's imagine we have 10 dollars and want to divide them equally among 3 friends. What happens here? Can we divide without anything left over?' Here, the idea is for students to understand that even when dividing money, it is not always possible to divide exactly, and what is left is called the 'remainder'.

4. Contextualization: The teacher explains to the students that division with remainder is very important in various everyday situations. For example, in dividing candies at a birthday party, in sharing toys among friends, or even in dividing time when we want to know how many days are left until the weekend, for instance. The goal is to make students realize the relevance and applicability of the content that will be taught.

5. Curiosity: To spark students' interest, the teacher can share curiosities about division with remainder. For example, they can mention that this idea of remainder in division is very old and was already used by the Egyptians and Babylonians over 4,000 years ago. Additionally, they can point out that in mathematics, the remainder of the division is always smaller than the divisor, and if the remainder is zero, we say the division is exact.

By the end of the introduction, students should be familiar with the concept of division remainder, understand the importance and applicability of this concept, and be motivated to learn more about the subject.

Development (20 - 25 minutes)

1. Theory of Division Remainder (5 - 7 minutes)

   • The teacher begins by explaining that division with remainder occurs when we cannot divide one number exactly by another, meaning there is always a part that is not enough to be a 'whole part'.
   • Next, the teacher should introduce the symbol for the division remainder (%), explaining that it is used to represent the number left after the division.
   • Providing examples of the concept of division remainder with simple situations, such as dividing candies among friends or dividing tasks in a group, will help make the concept more concrete for students.

2. Calculation of Division Remainder (5 - 7 minutes)

   • The teacher should teach students how to calculate the remainder of a division. Initially, the focus should be on examples where the division is exact, so that students understand the notion that when nothing is left, the remainder is zero.
   • Subsequently, the teacher should introduce examples of division with remainder, demonstrating how to identify the remainder and the whole part of the quotient.
   • Practical exercises are recommended, using small numbers and situations that are close to students' daily lives, in order to facilitate the understanding of the concept.

3. Properties and Importance of Division Remainder (5 - 7 minutes)

   • The teacher should discuss with the class some properties of the division remainder, such as the fact that it is always a number smaller than the divisor and that the remainder plus the product of the quotient by the divisor is equal to the dividend.
   • The teacher should emphasize the importance of the division remainder, showing how it is used in various everyday situations, such as in dividing candies among friends, sharing tasks, dividing money, counting days until an event, among others.

By the end of this stage, students should be able to understand the concept of division remainder, identify and calculate the remainder of a division, and understand the importance and applicability of this concept in daily life.

Feedback (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes)

   • The teacher should gather the class and promote a group discussion about the solutions found for the problems proposed during the lesson.
   • Each group of students should present their solutions and the reasoning used to reach them. The teacher should encourage all students to participate and explain their ideas.
   • During the discussion, the teacher should highlight the most effective problem-solving strategies, correct any possible misconceptions, and reinforce the important concepts covered in the lesson.

2. Connection to Theory (3 - 5 minutes)

   • After the discussion, the teacher should ask questions that connect the practical activity with the theory presented in the lesson. For example, 'How did you identify the division remainder? What does this mean in practice?'
   • The teacher can also suggest that students reflect on how they could use the concept of division remainder in everyday situations. For instance, 'How can what we learned today help us divide a cake at a birthday party?' or 'How could the division remainder help us organize the line for a game at school?'

3. Final Reflection (2 - 3 minutes)

   • To conclude the lesson, the teacher should propose that students reflect for a minute on what they learned in the lesson.
   • The teacher can ask two simple questions to guide students' reflection: 'What did you find most interesting about what we learned today?' and 'How can you use what we learned today in everyday situations?'
   • The teacher can ask some students to share their answers with the class, reinforcing the idea that all students have valuable contributions to make and that learning is a continuous process.

By the end of this stage, students should be able to articulate what they learned in the lesson, connect theory with practice, and reflect on how they can apply what they learned in everyday situations.

Conclusion (5 - 10 minutes)

1. Lesson Summary (2 - 3 minutes)

   • The teacher should start the conclusion of the lesson by briefly summarizing the main concepts that were covered. They should reinforce the understanding of what a 'division remainder' is and how to calculate it, explaining again that it is what is left when an exact division is not possible.
   • Additionally, the teacher should recap the properties of the division remainder, such as always being smaller than the divisor, and the importance of this concept in everyday life.

2. Connection of Theory with Practice (1 - 2 minutes)

   • The teacher should recall how the practical activities carried out during the lesson helped to illustrate and consolidate the understanding of the theoretical concepts. They can mention the problems solved in groups, the strategies used by students, and how they applied the concept of division remainder to solve them.

3. Extra Materials (1 - 2 minutes)

   • The teacher can suggest extra materials for students who wish to deepen their knowledge on the subject. This may include books, online games, educational videos, or even activities to do at home with family.
   • For example, the teacher can recommend a board game involving division remainder, an animated video explaining the concept in a playful way, or a book of mathematical stories addressing the topic.

4. Importance of Division Remainder (1 - 2 minutes)

   • Finally, the teacher should reinforce the importance of the content learned for students' lives, explaining that division with remainder is a fundamental mathematical skill used in various everyday situations, from sharing candies to dividing tasks.
   • Additionally, the teacher should emphasize that understanding the concept of division remainder helps develop skills such as logical reasoning, problem-solving, and the ability to organize and analyze information.

By the end of this stage, students should have consolidated their understanding of the concept of division remainder, understood the importance and applicability of this concept, and be motivated to continue learning about the subject.