Objectives (5 minutes)

1. Understand the concept of division remainders: Students should be able to understand what remainders in division are, which is the number left over when one number cannot be evenly divided by another. They should be able to identify the remainder in a problem and understand how it affects the answer.

2. Solve problems with division remainders: Students should be able to apply the concept of division remainders to solve mathematical problems. They should be able to use division to solve everyday situations and interpret the meaning of the remainder in the problem resolution.

3. Develop logical reasoning skills: Through solving problems involving division remainders, students should develop logical and critical thinking skills. They should be able to think logically and systematically to arrive at the correct answer.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher should start the lesson by briefly reviewing the concepts of addition, subtraction, and multiplication, which are fundamental to understanding division. The teacher can propose some simple problem situations involving these operations to reinforce students' understanding.

2. Contextualized problem situations: The teacher should then present two problem situations that can be solved with division and that are relevant to students' lives. For example: "If we have 20 candies to distribute equally among 5 children, how many candies will each child receive? And how many candies will be left over?" and "If a box has 32 chocolates and we can put 8 chocolates in each bag, how many bags can we make? And how many chocolates will be left over?".

3. Introduction to the topic of the day: The teacher should then introduce the topic of the lesson, division remainders, explaining that sometimes, when we divide one number by another, we do not get an exact division, and a number called the remainder is left over. The teacher can give simple examples, such as: "If we divide 10 candies equally among 3 children, each child will receive 3 candies, and there will still be 1 candy left. This 1 is the remainder of the division." and "If we divide 20 chocolates equally among 7 bags, each bag will receive 2 chocolates, and there will still be 6 chocolates left. This 6 is the remainder of the division.".

4. Contextualization of the topic's importance: The teacher can then explain that understanding division remainders is important for solving everyday problems, such as dividing a quantity of objects equally, or distributing tasks among a number of people. Additionally, the teacher can mention that division with remainder is also used in other areas, such as computer programming, financial mathematics, and many other situations.

Development (20 - 25 minutes)

1. Fun Remainder Game (10 - 15 minutes)

   • The teacher divides the class into groups of five students and distributes a set of objects, such as colored pencils or building blocks, to each group.

   • Then, the teacher presents a problem that involves dividing the quantity of objects in the group equally among the students. For example: "We have 17 building blocks and want to divide them equally among 5 students. How many blocks will each student receive?".

   • The teacher then instructs the students to solve the problem, but with a condition: they cannot use division, they have to find the answer through successive subtractions. This is for the students to understand how the concept of remainder relates to other mathematical operations.

   • The group that correctly solves the problem first earns a point. The teacher repeats the process with other problems, always reminding students to consider what happens when they cannot divide all objects equally.

   • At the end of the game, the group with the most points wins.

2. Party Remainder Activity (10 minutes)

   • The teacher starts the activity by dividing the class into groups of four or five students and distributes a bag with 30 candies to each group.

   • Then, the teacher tells the students that each candy represents a guest at a birthday party, and they have to divide the candies equally among the guests. The challenge is that each guest can only receive up to 6 candies, so they will have to count how many guests they can serve and how many candies will be left over.

   • The students then start dividing the candies, recording the amount of candies each guest receives and the amount left over. The teacher circulates around the room, assisting the groups when necessary and checking progress.

   • After a few minutes, the teacher stops the activity and asks each group to present their results. The teacher then writes the groups' answers on the board so that everyone can compare the solutions.

   • The teacher then reinforces the concept of remainder, pointing out that the number of candies left over is the remainder of the division.

   • The teacher can conclude the activity by reinforcing that mathematics is a very useful tool for solving real-life problems, such as planning a party and ensuring that all guests have a fair number of candies.

3. Choice Remainder Activity (10 minutes)

   • The teacher divides the class into groups and distributes a box with numbered chips from 1 to 20 to each group.

   • Then, the teacher presents a problem: "In school, there are 20 children and 5 toys available to play with. How many toys can each child choose? Will there be any toy that no child can choose? And if we have 6 toys available, what changes in the situation?".

   • The students then solve the problem, dividing the chips equally among the group members and observing what happens when it is no longer possible to divide equally.

   • After a few minutes, the teacher stops the activity and asks each group to present their results. The teacher can then reinforce the concept of remainder, pointing out that it is the number that cannot be divided equally and that, in this case, represents the toys that were left over and could not be chosen by any child.

   • The teacher can conclude the activity by reinforcing that the concept of division remainders is very useful for solving everyday problems and that mathematics is a powerful tool to help us understand the world around us.

Teachers can choose one or more activities to carry out in the classroom, depending on the available time and the students' learning pace. The activities were designed to be interactive, engaging, and to promote collaboration among students. Additionally, the activities are designed to reinforce the understanding of the concept of division remainders and its application in everyday situations.

Feedback (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes)

   • The teacher gathers all students in a large discussion circle and asks each group to share their solutions to the activities carried out.

   • During the presentation, the teacher encourages students to explain their reasoning, how they arrived at the answer, and how they identified the division remainder.

   • The teacher can also ask students to express their difficulties or doubts encountered during the activity, so that these can be clarified and resolved.

2. Connection to Theory (3 - 5 minutes)

   • After the groups' presentations, the teacher revisits the theoretical concepts of the lesson, reinforcing what division remainders are and how they are important for problem solving.

   • The teacher can use the solutions presented by the students to illustrate how the concept of division remainder is applied in practice, reinforcing the idea that the remainder of division is applied in real-life situations.

3. Individual Reflection (2 - 3 minutes)

   • The teacher proposes that students reflect on what they learned in the lesson. To do this, the teacher asks two simple questions:

     1. "How can you use what you learned today about division remainders in your daily life?"
     2. "What was the most challenging part of today's lesson and why?"

   • Students have a minute to think about their answers and then have the opportunity to share their reflections with the class, if they wish.

4. Teacher Feedback (1 minute)

   • The teacher concludes the lesson by giving overall feedback on the students' performance, highlighting strengths and areas that still need to be worked on.

   • The teacher encourages students to continue practicing what they have learned, emphasizing that practice is essential for improving mathematical skills.

This feedback stage is crucial to consolidate students' learning, allowing them to reflect on what they have learned and how they can apply this knowledge in everyday situations. Additionally, group discussion and teacher feedback help identify possible learning gaps and guide the planning of future lessons.

Conclusion (5 - 7 minutes)

1. Lesson Summary (2 - 3 minutes)

   • The teacher begins the conclusion by recalling the main points covered during the lesson. He emphasizes that division is a mathematical operation that helps us share or group quantities equally. He also reinforces that sometimes, when we divide, it is not possible to obtain an exact division, and a number called the remainder is left over. The teacher can give simple examples to recap, such as: "If we divide 10 candies equally among 3 children, each child will receive 3 candies, and there will still be 1 candy left. This 1 is the remainder of the division." and "If we divide 20 chocolates equally among 7 bags, each bag will receive 2 chocolates, and there will still be 6 chocolates left. This 6 is the remainder of the division.".

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

   • The teacher then highlights how the lesson connected theory and practice, explaining that students had the opportunity to apply the concept of division remainders in everyday situations, such as dividing candies at a birthday party or toys among children at school. He also mentions that by solving practical problems, students were able to better understand the importance and usefulness of mathematics in their lives.

3. Extra Materials (1 minute)

   • The teacher then suggests some extra materials for students who wish to deepen their knowledge of division remainders. He can suggest age-appropriate math books, online games involving division with remainder, or educational videos available on the internet. He can also provide some exercise sheets for students to practice at home.

4. Importance of the Subject (1 minute)

   • Finally, the teacher concludes the lesson by reinforcing the importance of what was learned. He explains that the ability to divide and understand division remainders is essential for solving everyday problems, making more complex calculations, and better understanding the world around us. He also encourages students to continue practicing, reminding them that practice is essential for improving mathematical skills.

The conclusion is a crucial stage to consolidate students' learning, summarize the main points of the lesson, and encourage continuous study. Additionally, by connecting theory with practice and highlighting the importance of the subject, the teacher helps students understand the relevance of what they have learned and apply it in their lives.