Objectives (5 minutes)

1. Understand the concept of even and odd functions, identifying the relationship between even and odd numbers.
2. Identify if a number is even or odd through the analysis of a graphic representation.
3. Develop the skill of solving practical problems that involve classifying numbers as even or odd.

Secondary objectives:

• Develop critical and logical-mathematical thinking skills.
• Foster students' active participation through the flipped classroom methodology.
• Encourage the application of mathematical knowledge in everyday situations.

During this stage, the teacher should clearly present the Learning Objectives of the lesson, explaining the importance of learning about even and odd functions and how it relates to the real world. The teacher should also encourage students to ask questions and express their expectations for the lesson.

Introduction (10 - 15 minutes)

1. Review of prior concepts (3 minutes): The teacher should begin the lesson by briefly reviewing the concepts of even and odd numbers. They can do this through direct questions to students, asking them to recall which numbers end in zero, two, four, six, and eight (even numbers) and which numbers end in one, three, five, seven, and nine (odd numbers). This review is essential for students to be able to understand the concept of even and odd functions.

2. Contextualization (4 minutes): Next, the teacher should present two problem situations that help contextualize the topic of the lesson. For example, they could ask students if they have ever noticed a pattern in even and odd numbers. Or ask them to think about how even and odd numbers are used in our everyday lives, such as when counting objects in pairs or odds. This step is important for students to realize the relevance of the topic to their everyday lives.

3. Introduction to the topic (5 minutes): The teacher should then introduce the concept of even and odd functions. To do this, they can present two problem situations: the first, involving an even function, and the second, an odd function. For example, they could show students a sequence of numbers and ask them if they can see a pattern. Then, they could reveal that it is an even function and explain what that means. Then, they could do the same with an odd function. The teacher should use simple, clear examples, making sure that all students are following along.

4. Captivating the students' attention (3 minutes): To make the Introduction more interesting, the teacher could share some fun facts about even and odd functions. For example, they could mention that all numbers ending in 0, 2, 4, 6, or 8 are divisible by 2, and therefore, even. Or they could talk about the fact that the sum of two even numbers is always even, the sum of two odd numbers is always even, and the sum of an even and odd number is always odd. The teacher should try to pique students' curiosity, setting the stage for a deeper exploration of the topic.

Development (20 - 25 minutes)

1. Activity "Even or Odd?" (10 minutes): In this activity, students will be challenged to classify a series of numbers as even or odd. The teacher should divide the class into groups of 3 or 4 students and give each group a set of cards with numbers written on them. The numbers should range from 1 to 20. Students should then discuss with each other and agree on whether the number on the card is even or odd. Then, they should justify their choices. The teacher should circulate around the room, monitoring the discussions and clarifying any doubts. At the end of the activity, each group should present a general Conclusion about the classification of the numbers.

   • Step by step:
     1. The teacher divides the class into groups and gives each group a set of cards with numbers written on them.
     2. The students, in their groups, discuss whether the number on the card is even or odd.
     3. Each group presents its Conclusion, justifying it.
     4. The teacher monitors the discussions, clarifies any doubts, and makes relevant observations.

2. Activity "Even and Odd Functions" (10 - 15 minutes): In this activity, students will explore the relationship between even and odd numbers through a graphical representation. The teacher should provide each group with a sheet of paper, markers, and rulers. Students should draw two Cartesian axes on their sheets of paper. On one axis, they should mark the even numbers from 1 to 10, and on the other, the odd numbers from 1 to 10. Then, they should draw a straight line connecting each even number on the first axis to its corresponding odd number on the second axis. The teacher should guide the students during the activity, clarifying any doubts and ensuring that everyone is following along.

   • Step by step:
     1. The teacher provides each group with a sheet of paper, markers, and rulers.
     2. Students draw two Cartesian axes on their sheets of paper.
     3. On one axis, they mark the even numbers from 1 to 10, and on the other, the odd numbers from 1 to 10.
     4. They draw a straight line connecting each even number on the first axis to its corresponding odd number on the second axis.
     5. The teacher guides the students during the activity, clarifies any doubts, and makes relevant observations.

3. Activity "Even and Odd Functions in Everyday Life" (5 minutes): In this activity, students should think about everyday situations that involve the classification of numbers as even or odd. The teacher should encourage students to be creative and to think outside the box. For example, students could think about how even and odd numbers are used in games, in counting objects, in computer programming, among others. This activity aims to reinforce the relevance of the topic and encourage the application of knowledge in practical situations.

   • Step by step:
     1. The teacher asks students to think about everyday situations that involve the classification of numbers as even or odd.
     2. Students, in their groups, discuss and write down their ideas.
     3. A representative from each group shares the ideas with the class.
     4. The teacher makes relevant observations and highlights the application of knowledge in practical situations.

During Development, the teacher should ensure that all students actively participate in the activities, clarifying doubts and encouraging discussion.

Feedback (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes): The teacher should promote a group discussion, where each team shares their conclusions from the activities. This allows students to learn from each other, to be exposed to different ways of approaching the same problem, and to feel part of a learning community. The teacher should ensure that all students have the opportunity to speak and that the discussions are respectful and productive.

   • Step by step:
     1. The teacher asks each group to share their conclusions or solutions to the activities.
     2. A representative from each group presents their group's conclusions or solutions.
     3. The teacher facilitates the discussion, asking questions to clarify students' reasoning, encouraging everyone's participation, and ensuring that the discussion stays on topic.

2. Connection with the Theory (3 - 5 minutes): After the discussions, the teacher should make the connection between the activities carried out and the theory learned. They should recap the main concepts of even and odd functions and demonstrate how students applied these concepts during the activities. The teacher should use examples from the activities to illustrate the practical application of the theory.

   • Step by step:
     1. The teacher recaps the main concepts of even and odd functions.
     2. The teacher demonstrates how students applied these concepts during the activities.
     3. The teacher uses examples from the activities to illustrate the practical application of the theory.

3. Reflection (2 - 3 minutes): To conclude the lesson, the teacher should ask students to reflect silently for a minute on what they have learned. Then, they should ask questions to guide students' reflection, such as: "What was the most important concept you learned today?" and "What questions do you still have?" The teacher should encourage students to share their reflections and questions, creating an open and receptive learning environment.

   • Step by step:
     1. The teacher asks students to reflect silently for a minute.
     2. The teacher asks questions to guide students' reflection.
     3. Students share their reflections and questions.
     4. The teacher answers students' questions and provides feedback on students' reflections.

During Feedback, the teacher should be attentive to identify any points of confusion or misunderstanding and address them immediately. The teacher should also encourage students to continue exploring the topic outside the classroom, for example, through additional readings or problem-solving practice.

Conclusion (5 - 7 minutes)

1. Summary and Recap (2 - 3 minutes): The teacher should begin the Conclusion stage by briefly summarizing the main points covered in the lesson. They should recap the definition of even and odd functions, the relationship between even and odd numbers, and how to identify if a number is even or odd through its graphical representation. The teacher should also recall the main conclusions from the activities carried out, highlighting the patterns and relationships that students were able to identify.

   • Step by step:
     1. The teacher summarizes the main points covered in the lesson.
     2. The teacher recaps the definition of even and odd functions, the relationship between even and odd numbers, and how to identify if a number is even or odd through its graphical representation.
     3. The teacher recalls the main conclusions from the activities carried out.

2. Connection with Practice and Everyday Life (1 - 2 minutes): Next, the teacher should emphasize how the concept of even and odd functions applies in everyday life. For example, they could mention that classifying numbers as even or odd is used in various everyday situations, such as counting objects, in computer programming, among others. The teacher should highlight that mathematics is not just a theoretical discipline, but a practical tool that helps us understand and deal with the world around us.

   • Step by step:
     1. The teacher emphasizes how the concept of even and odd functions applies in everyday life.
     2. The teacher mentions examples of everyday situations that involve classifying numbers as even or odd.
     3. The teacher highlights the importance of mathematics as a practical tool for understanding and dealing with the world around us.

3. Extra Materials (1 - 2 minutes): The teacher should then suggest extra materials for students who want to deepen their understanding of the topic. These materials could include books, websites, videos, and digital games that explore the concept of even and odd functions in different and interesting ways. The teacher should briefly explain what students can expect from each material and how they can access it.

   • Step by step:
     1. The teacher suggests extra materials for students who want to deepen their understanding of the topic.
     2. The teacher briefly explains what students can expect from each material and how they can access it.

4. Importance of the Subject (1 minute): To conclude, the teacher should reinforce the importance of the topic presented for the students' everyday lives. For example, they could mention that the ability to identify if a number is even or odd is useful in various situations, such as solving mathematical problems, in computer programming, in understanding statistics, among others. The teacher should end the lesson by encouraging students to continue exploring the world of mathematics and to apply what they have learned in their everyday lives.

   • Step by step:
     1. The teacher reinforces the importance of the topic presented for the students' everyday lives.
     2. The teacher ends the lesson by encouraging students to continue exploring the world of mathematics and to apply what they have learned in their everyday lives.