Objectives (5 - 10 minutes)

1. Familiarize students with the concept of numerical sequences, which can be progressive (addition) or regressive (subtraction).
2. Teach students to create simple numerical sequences, both for addition and subtraction, using natural numbers.
3. Develop students' ability to identify the rule of formation of a numerical sequence, whether by addition or subtraction.

These objectives will be achieved through practical activities and games that encourage participation and collaboration among students. The teacher will provide continuous guidance and feedback to ensure that all students are understanding the material.

Introduction (10 - 15 minutes)

1. Review of contents: The teacher will start by reviewing the students on the basic concepts of addition and subtraction. This can be done through simple questions and review activities, such as solving addition and subtraction problems with small numbers. The teacher can also project examples on the board and ask students to solve them individually in their notebooks.

2. Problem situations: The teacher will propose two problem situations involving the use of numerical sequences. For example:

   • 'If I have 5 candies and I get 2 more candies each day, how many candies will I have after 7 days?'
   • 'If I have 10 dollars and I spend 3 dollars each day, how much money will I have left after 5 days?'

3. Contextualization: The teacher will explain that numerical sequences are used in everyday situations, such as planning a week of snacks at school or managing the money in a piggy bank. The teacher can use concrete examples, such as a shopping list, or situations that students can experience, such as counting down to the holidays.

4. Introduction of the topic: The teacher will introduce the topic of the lesson, numerical sequences, explaining that they are lists of numbers that follow a specific rule. The teacher can use the board to write some simple sequences, such as 1, 2, 3, 4, 5 (addition of 1) or 10, 9, 8, 7, 6 (subtraction of 1). To make the introduction more interesting, the teacher can ask students to guess the next sequence of numbers.

Development (20 - 25 minutes)

For this development stage, the teacher will propose two practical and playful activities involving the creation and resolution of numerical sequences. The teacher can choose one of the activities or, if there is enough time, perform both.

Activity 1: 'The Sequence Factory' (10 - 15 minutes)

1. The teacher divides the class into groups of 4 to 5 students and gives each group a sheet of paper, a pencil, and a set of number cards (1 to 10) or small pieces of paper with numbers written on them.

2. The students' task is to create numerical sequences, either by addition or subtraction, using the numbers on the cards. They must think of a rule for the sequence (for example, 'we will add 2 to each number') and write the sequence on the sheet of paper.

3. The teacher circulates around the room, guiding the groups and ensuring that all students are actively participating. Providing some initial examples to guide the students may be helpful.

4. Once the groups have created their sequences, they should move on to the next step - 'The Sequence Factory'. Each group will exchange their sheets of paper with another group, which will have the task of identifying the rule of the sequence and predicting the next numbers.

5. After a set time, the groups share their sequences and the rules they discovered. The teacher can use this discussion to reinforce the concepts presented and emphasize the importance of identifying the rule of the sequence.

Activity 2: 'Sequence Hunt' (10 - 15 minutes)

1. The teacher hides several number cards (1 to 10) around the classroom. The numbers should be arranged randomly.

2. The teacher divides the class into groups and gives each group a list of numerical sequences to find. For example, the list may contain sequences like '2, 4, 6, 8...' (addition of 2) or '10, 7, 4, 1...' (subtraction of 3).

3. The groups must search for the number cards around the room and organize the numbers found according to the sequences on the list. They must identify the rule of each sequence and predict the next number.

4. The teacher circulates around the room, assisting the groups in finding the numbers and identifying the rules of the sequences.

5. Once all groups have found the sequences, they should share their findings with the class, explaining the rule of each sequence and the next number.

During these activities, the teacher must ensure that all students are involved and understanding the concepts presented. The teacher should encourage discussion and collaboration among students, as well as provide constant feedback to reinforce learning.

Feedback (10 - 15 minutes)

1. Group Discussion: The teacher will gather all students in a large circle for a group discussion. Each group of students will have the opportunity to share the sequences they created and the rules they identified. The teacher will ask questions to ensure that all students understand the rules of the sequences presented. Additionally, the teacher may ask students to explain how they arrived at their conclusions, encouraging reflection and critical thinking. (5 - 7 minutes)

2. Connection to Theory: Next, the teacher will make the connection between the practical activities and the theory of numerical sequences. The teacher will explain that the sequences that students created and identified are examples of numerical sequences, which are lists of numbers that follow a specific rule. The teacher can use the board to write some of the sequences presented by the students and their corresponding rules, reinforcing the concept of addition and subtraction sequences. (3 - 5 minutes)

3. Individual Reflection: To conclude the lesson, the teacher will propose that students reflect individually on what they have learned. For this, the teacher will ask two simple questions:

   • 'What was the most challenging sequence you had to create or identify? Why?'
   • 'How can you use what you learned today about addition and subtraction sequences in everyday situations?'

   Students will have a minute to think about their answers, and then they will have the opportunity to share them with the class, if they wish. The teacher should remind students that all answers are valid and that the important thing is to reflect on what was learned. (2 - 3 minutes)

This feedback stage is crucial to consolidate students' learning. The group discussion allows students to learn from each other and see different ways to approach the same problem. The connection to theory helps students understand the relevance of the practical activities for the study of numerical sequences. And individual reflection helps students internalize what they have learned and apply that knowledge in other situations.

Conclusion (5 - 10 minutes)

1. Recapitulation: The teacher will begin the conclusion of the lesson by summarizing the main points covered. This will include the definition of numerical sequences, the distinction between addition and subtraction sequences, and the importance of identifying the rule of a sequence. The teacher can do this by recalling the sequences created by students during the practical activities and discussed during the feedback stage. (2 - 3 minutes)

2. Theory-Practice Connection: The teacher will emphasize how the lesson connected mathematical theory with practice. The situations in which students were able to apply the concepts of addition and subtraction sequences will be highlighted, whether through the creation of numerical sequences or in the identification of the rules of sequences created by other groups. The teacher can cite specific examples of activities to illustrate this connection. (2 - 3 minutes)

3. Supplementary Materials: To deepen students' understanding of the lesson's topic, the teacher will suggest some supplementary materials. These may include:

   • Textbooks: The teacher may indicate specific pages of textbooks that address the subject of numerical sequences.
   • Online games: The teacher may suggest online educational games that allow students to practice creating and identifying numerical sequences in a fun way.
   • Homework exercises: The teacher may prepare a list of simple exercises for students to practice at home. These exercises may include creating addition and subtraction sequences and identifying the rules of given sequences. (2 - 3 minutes)

4. Importance of the Subject: Finally, the teacher will explain the importance of learning about numerical sequences. It will be emphasized how this knowledge can be applied in various everyday situations, from planning a weekly routine to managing expenses. Additionally, the teacher will reinforce that the ability to identify and create numerical sequences is fundamental for the development of other mathematical competencies, such as problems solving and pattern recognition. (1 minute)

The conclusion of the lesson is an essential stage to consolidate students' learning. The recapitulation helps reinforce the concepts learned, the theory-practice connection allows students to see the relevance of what they have learned, and the supplementary materials provide resources for students to continue learning about the subject. Furthermore, by explaining the importance of the subject, the teacher motivates students to engage more in the study of numerical sequences.