Objectives (5 - 7 minutes)

1. Introduce the concept of rational numbers in a playful and interactive way, in order to spark students' interest and active participation.

2. Provide students with a learning environment that allows them to identify, name, and compare rational numbers using manipulative teaching materials.

3. Develop students' ability to solve simple problem situations involving rational numbers, encouraging them to use counting strategies and logical reasoning.

Secondary Objectives:

• Encourage teamwork and cooperation among students through activities that promote interaction and communication among them.

• Stimulate students' critical thinking by challenging them to justify their answers and reflect on problem-solving processes.

• Foster a love for mathematics, showing students that rational numbers are not just theoretical abstractions, but useful tools for solving everyday problems.

Introduction (10 - 12 minutes)

1. Recalling previous content: The teacher starts the lesson with a brief review of natural numbers, reminding students of what they are and some of their basic properties. For example, the teacher may ask for the students' help in counting objects in the classroom, emphasizing that this is a practical application of natural numbers.

2. Setting the problem: After the review, the teacher presents two problem situations involving the division of objects among people. In the first situation, there are 6 balls and 3 children, and in the second, there are 8 balls and 4 children. The teacher asks the students: 'How many balls will each child have?' The goal is to make students realize that division is not always exact, meaning there may be remainders.

3. Spark curiosity: The teacher then asks the students if they have ever stopped to think about what happens with the remainder when dividing one number by another. He proposes the following situation: 'If I have 7 candies and want to divide them equally between 2 friends, each will receive 3 candies. But what happens to the leftover candy?' The teacher uses this situation to arouse the students' curiosity and introduce the concept of rational numbers.

4. Contextualization: The teacher explains that the concept of rational numbers is very important because it helps us solve everyday problems, such as dividing candies among friends or calculating the amount of food for a certain number of people at a party. Additionally, the teacher emphasizes that rational numbers are not just theory, but are very present in practice, such as in the prices of products at the supermarket, for example.

5. Introduction of the topic: The teacher then introduces the concept of rational numbers, explaining that it is formed by an integer part and a fractional part (decimal numbers), and that there is always a division relationship between these two parts. To illustrate, the teacher writes on the board some examples of rational numbers, such as 1/2, 2/3, 5/4, 1.5, 3.25, 0.25, and asks the students if they can identify the integer part and the fractional part in each of them. The teacher also clarifies that rational numbers include integers, such as 1, 2, 3, and that natural numbers are a specific type of rational number.

6. Capturing students' attention: To make the introduction of the concept of rational numbers more interesting, the teacher can share some curiosities. For example, he can mention that rational numbers are called that because they are 'rational,' meaning they can be expressed as a ratio (or fraction) of two integers. Furthermore, the teacher can show students that rational numbers can be represented not only in fraction form, but also in decimal form, and that these two forms are equivalent. For instance, the teacher can write the fraction 1/2 and the decimal 0.5 on the board, and ask the students if they can identify the relationship between the two representations.

Development (20 - 25 minutes)

The teacher can choose from the following playful and practical activities to consolidate the concept of rational numbers with students. Note that each activity is set with an estimated time, but the teacher should adjust the time as needed based on the class's progress and needs.

Activity 1: 'Adventure in the Treasure of Rational Numbers' (10 - 12 minutes)

1. The teacher divides the class into groups of four students and provides each group with a set of numbered cards. These cards should contain various rational numbers, both in fraction and decimal form (for example, 1/2, 3/4, 1.5, 2.25, 0.75, etc.). The number of cards should be sufficient for each student in the group to have at least one card to manipulate.

2. The teacher explains that the students will be participating in an adventure in the 'Treasure of Rational Numbers.' They must use the cards to solve a mathematical challenge and discover the combination of the code that will open the treasure.

3. The teacher presents the challenge: 'The treasure will only be revealed when all the rational numbers are in ascending order. Use your cards and work together to organize the numbers from smallest to largest.'

4. The teacher circulates around the room, assisting the groups and asking questions to guide the students' reasoning. For example: 'What is the smallest rational number you have? And the largest? And now, what is the next number in the sequence?'

5. When the groups finish, they reveal the code combination and open the 'Treasure of Rational Numbers,' which can be a small reward or an extra mathematical challenge.

Activity 2: 'Building a Tower of Rationals' (8 - 10 minutes)

1. The teacher distributes to each group of students a set of blocks. Each block has a fraction or decimal number written on it (for example, 1/4, 1/2, 3/4, 1.5, 2.25, etc.).

2. The teacher explains that the students need to work together to build a tower using the blocks. However, there is a rule: the tower must be assembled in ascending order, from the smallest to the largest rational number.

3. The students start building their towers, discussing among themselves the best way to organize them. The teacher circulates around the room, asking questions to guide the groups' reasoning, such as: 'What is the smallest rational number you have? And the largest? And now, what is the next number in the sequence?'

4. When all groups have completed their towers, the teacher invites each group to explain the strategy used and why each block was placed in a certain position.

Activity 3: 'The Crossing of Rationals' (7 - 8 minutes)

1. The teacher draws a straight line on the floor or on the board, representing a 'river.' At one end of the 'line,' the teacher draws a 'boat,' and at the other end, a 'port.'

2. The teacher distributes to each group of students a series of cards containing rational numbers, both in fraction and decimal form. The numbers should vary so that students have to make decisions about the best order to cross the river.

3. The teacher explains that the students will be 'sailors' and must help the 'captain' (who is the teacher) cross the river, but they can only take one rational number at a time in the boat. The goal is to reach the port with the numbers in ascending order.

4. The teacher starts the 'crossing' by choosing a rational number and placing the corresponding card in the 'boat.' The students decide if this is the best time to cross or if they should wait for a larger/smaller number. The teacher justifies the 'captain's' decisions based on the 'sailors' suggestions.

5. The process is repeated until all numbers have crossed the 'river.' At the end, the teacher asks the students to organize the numbers from smallest to largest and explain their decisions.

These activities are just suggestions, and the teacher can choose the one that best suits the class. The important thing is that they are practical, playful activities that encourage cooperation and logical reasoning among students. At the end, the teacher should set aside time for group discussion and presentation of solutions, reinforcing the concepts learned during the activities.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): After completing the activities, the teacher gathers all students in a large circle for a group discussion. Each group has the opportunity to share the solutions or strategies they found during the activities. The teacher can ask questions to promote reflection, such as: 'Why did you decide to place this number here?' or 'What did you notice when comparing the numbers in your solutions?' The goal is to allow students to learn from each other and consider different approaches to solving mathematical problems.

2. Connection with Theory (2 - 3 minutes): After the discussion, the teacher reviews the solutions and strategies presented by the students and relates them to the theoretical concept of rational numbers. For example, he can ask: 'Did you notice that, to organize rational numbers in ascending order, it is necessary to compare them? How did you make this comparison?' The teacher reinforces that the ability to compare and order rational numbers is essential to understand the concept and to solve mathematical problems.

3. Individual Reflection (2 - 3 minutes): To conclude the lesson, the teacher proposes that students reflect for a minute on what they have learned. He asks two simple questions, which students should answer mentally:

   • 'What did you enjoy learning most about rational numbers today?'

   • 'How can you use what you learned today to solve mathematical problems at home or at school?'

4. Sharing Reflections (1 - 2 minutes): The teacher then invites some students to share their reflections with the class. This is an opportunity for students to practice oral expression and for the teacher to assess students' understanding of the lesson topic. Additionally, by listening to their classmates' reflections, students may be inspired to think more deeply about what they have learned.

This return is an essential step to consolidate learning, allow students to reflect on what they have learned, and how they can apply this knowledge in future situations. Furthermore, group discussion and individual reflection encourage students to become active learners, responsible for their own learning.

Conclusion (3 - 5 minutes)

1. Summary of Contents (1 - 2 minutes): The teacher begins the conclusion by recalling the main points covered during the lesson. He explains that rational numbers are those that can be expressed as a ratio of two integers, that is, in the form of a fraction. Additionally, the teacher highlights that rational numbers can also be represented in decimal form. The teacher can quickly review the concepts presented, asking students to identify rational numbers in examples on the board or in manipulative teaching materials.

2. Connection between Theory and Practice (1 minute): Next, the teacher emphasizes how the practical activities contributed to the understanding of the concept of rational numbers. He reinforces that the problem situations and challenges proposed in the activities allowed students to explore and apply theoretical concepts in a meaningful way. The teacher also mentions how group discussions and individual reflections helped reinforce students' understanding of the subject.

3. Additional Materials (1 minute): The teacher suggests some materials that students can explore at home to deepen their knowledge of rational numbers. This may include online games, educational apps, math books, or websites with interactive activities. For example, the teacher may recommend the use of apps that allow students to practice comparing and ordering rational numbers in a fun and interactive way.

4. Importance of the Subject (1 minute): Finally, the teacher emphasizes the importance of the subject for students' everyday lives. He explains that knowledge of rational numbers is essential for solving daily problems, such as dividing objects among people, calculating prices at the supermarket, or measuring ingredients for a recipe. Additionally, the teacher highlights that the ability to compare and order rational numbers is an essential tool for developing logical and critical thinking skills, which are increasingly valued in today's society.

This conclusion helps consolidate students' learning, reinforcing the main concepts and showing the relevance of the subject to real life. Furthermore, by suggesting additional materials, the teacher encourages students to continue exploring the topic outside the classroom, which can contribute to more autonomous and meaningful learning.