Objectives (5 - 7 minutes)

1. Introduce the concept of 'remainder' in division, which is the number left after equally distributing a number into equal parts.
2. Teach students how to calculate the remainder of a division, using practical and contextualized examples.
3. Provide students with the opportunity to practice the skill of calculating the remainder of division by solving problems and exercises in the classroom.

Secondary Objectives:

• Develop teamwork skills, as problem-solving will be done in groups.
• Stimulate logical and critical thinking through the resolution of mathematical problems.
• Promote active learning, making students the protagonists of their own learning.

Introduction (10 - 15 minutes)

1. To start the lesson, the teacher should review the basic concepts of division that were previously learned. This includes the definition of division, the terms used (dividend, divisor, quotient), and how to solve simple division problems.

2. Next, the teacher should present two problem situations involving division and the concept of remainder. For example:

   • 'Imagine we have 15 balls and want to divide them equally among 4 friends. Will all the balls be divided equally? Why?'
   • 'Now, if we have 16 balls and want to divide them equally among 4 friends, what happens? Will there be balls that are not divided equally? Why?'

3. The teacher should then contextualize the importance of the concept of remainder in students' daily lives. For example, it can be mentioned that when dividing a cake for the family, not all slices will always be the same size, or when sharing toys among friends, not everyone will always have the same quantity. This illustrates the need to understand the concept of remainder in division.

4. To introduce the topic in a playful and interesting way, the teacher can suggest two mathematical games involving the concept of remainder.

   • 'Division Remainder Game': Students form groups, and the teacher gives a quantity of objects for each group to divide equally. The group with the largest remainder wins.
   • 'Mathematical Puzzle': The teacher gives a quantity of objects to divide among the students, but one or more objects cannot be divided equally. The students must figure out who will get the remaining object and explain why.

With this introduction, students will be prepared to deepen their understanding of the concept of remainder in division and how to calculate it.

Development (20 - 25 minutes)

1. Now, the teacher should propose practical activities for students to explore and better understand the concept of remainder in division.

   • Activity 1: 'Garden Remainders' - The teacher can create cards with drawings of flowers and stones. Students must divide these cards equally among the members of their group. The group with the most 'remainders' (stones) at the end wins. During the activity, the teacher should guide and question the students about the division process and the definition of remainder.

   • Activity 2: 'Divided Cakes' - The teacher can bring toy cakes and ask students to divide the slices equally among the members of their group. The group with the most 'remainders' (pieces of cake that were not divided equally) at the end wins. Again, it is important for the teacher to guide and question the students about the division process and the definition of remainder.

2. After the practical activities, the teacher should return to the classroom discussion. Students should explain how they reached their conclusions, sharing their strategies and thoughts. The teacher should encourage an open and respectful discussion, valuing all contributions from the students.

3. Next, the teacher should introduce the theory of calculating the remainder in division. Explain that the remainder is what is left when a number cannot be divided equally by another.

4. The teacher should present examples of calculating the remainder in division using numbers that students are familiar with. For example, if the teacher divides 10 by 3, they should show that the quotient is 3 and the remainder is 1. The teacher should do this with several examples, varying the numbers and divisors, so that students can understand that the remainder can vary.

5. The teacher should then propose that students solve exercises to calculate the remainder in division. The exercises should start simple and become more complex according to the students' abilities. The teacher should circulate around the classroom, assisting students who need help and correcting the exercises.

6. To conclude the development stage, the teacher should ask students to share their answers and strategies for solving the exercises. The teacher should reinforce the key points of the lesson, such as the concept of remainder in division and the correct way to calculate it.

With this development, students will have had the opportunity to explore the concept of remainder in division in a practical and playful way, as well as deepen their knowledge through theory and exercise resolution.

Return (8 - 10 minutes)

1. The teacher should begin the return by providing a general review of the main points covered during the lesson. This can be done through questions directed at the students, asking them to summarize what they have learned. For example:

   • 'What is the remainder in division and why do we need it?'
   • 'How do we calculate the remainder in division?'
   • 'In what situations can there be a remainder in division?'

2. Next, the teacher should propose two problem situations to review the concept of remainder in division. These situations should be similar to those presented in the introduction but with different levels of difficulty so that students can apply what they have learned in a challenging way. For example:

   • 'We have 23 candies and want to divide them equally among 5 children. Will there be candies that are not divided equally? If so, how many?'
   • 'Now, if we have 32 pencils and want to divide them equally among 8 students, what happens? Will there be pencils that are not divided equally? If so, how many?'

3. Students should solve the problem situations in their groups, applying the knowledge acquired during the lesson. The teacher should circulate around the classroom, providing guidance and clarifying doubts if necessary.

4. Once the groups have solved the problem situations, the teacher should invite a representative from each group to share the solution and the strategy used. During the presentations, the teacher should encourage other students to ask questions and make comments, promoting a healthy and productive discussion.

5. To conclude the lesson, the teacher should contextualize the importance of what was learned, highlighting that the concept of remainder in division is an essential tool for solving more complex mathematical problems. Additionally, the teacher can mention that knowledge of division and remainder is useful in various everyday situations, such as when sharing candies, toys, or even when dividing tasks.

With this return, students will have the opportunity to consolidate what they have learned, applying the knowledge in a practical and contextualized way. Furthermore, the review and problem situations will allow the teacher to assess the effectiveness of the lesson and identify any areas that may need reinforcement or revision.

Conclusion (5 - 7 minutes)

1. The teacher should start the conclusion by reinforcing the main points covered during the lesson, emphasizing the importance of the concept of remainder in division. They can recap the definitions of dividend, divisor, quotient, and remainder, and how these elements relate in solving division problems. For example:

   • 'Remember that the dividend is the number we are dividing, the divisor is the number by which we are dividing, the quotient is the result of the division, and the remainder is what is left?'

2. Next, the teacher should highlight the skills and knowledge that students have acquired during the lesson. They can emphasize students' ability to divide numbers and determine the remainder autonomously, as well as the teamwork, logical thinking, and problem-solving skills that were developed during group activities. For example:

   • 'You now know how to divide numbers and determine the remainder. You have also demonstrated teamwork skills by solving problems in groups, and logical thinking by determining the best strategy to divide the objects in the activities.'

3. The teacher should then suggest complementary materials so that students can deepen their understanding of the topic. This may include math books, educational websites with games and interactive activities on division, and explanatory videos. The teacher can also suggest that students practice the skill of calculating the remainder in division at home by solving simple everyday problems. For example:

   • 'You can continue learning about division and remainder at home by solving division problems in your math books or on educational websites. You can also practice the skill of calculating the remainder by dividing toys or candies with your siblings or friends.'

4. Finally, the teacher should explain the importance of the topic for students' daily lives, highlighting that knowledge of division and remainder is useful in various everyday situations. For example, they can mention that understanding the concept of remainder can help to divide tasks equally among siblings or friends, to share a pizza fairly, or to solve more complex math problems. For example:

   • 'What we learned today is very useful for solving everyday problems. For example, if you have 10 stickers and want to divide them equally among 3 friends, now you know that each will get 3 stickers and there will be 1 left. That's the remainder of the division!'

5. The teacher should end the lesson by reinforcing that the knowledge acquired is important and useful, and that students can always rely on it in their future learning. For example:

   • 'Congratulations to everyone for the great work! What we learned today is very important and will help us in many other things we will learn. Always remember that the knowledge you acquire is a powerful tool that you can use to solve problems and discover new things.'

With this conclusion, students will have the opportunity to reinforce and expand their understanding of the topic, as well as feel motivated to continue learning and exploring mathematics. Additionally, the suggestion of complementary materials and the practical application of knowledge in everyday life will help consolidate the concepts learned.