Objectives (5 minutes)

1. Introduce the concept of symmetry to students, explaining that it is a concept that describes the equality of opposite sides or corresponding parts of a figure when folded along a specific line called the axis of symmetry.

2. Present the Cartesian plane as a tool that can be used to represent and identify symmetry in figures. Explain that the Cartesian plane is composed of two perpendicular lines, a horizontal one called the x-axis and a vertical one called the y-axis, intersecting at the point (0,0), called the origin.

3. Encourage students to recognize symmetry in various figures and to identify their axes of symmetry using the Cartesian plane.

Secondary Objectives:

• Develop students' logical reasoning and observational skills.
• Stimulate active participation and collaboration among students during practical activities.

Introduction (10 - 15 minutes)

1. Content Review: The teacher starts the lesson by reviewing with students previously learned content that is fundamental for understanding symmetry in the Cartesian plane. This content may include:

   • Numbers and number lines: the concept of positive and negative numbers, the idea that numbers can be represented on a line called a number line, and the location of points on this line.
   • Basic geometry: the concept of shape, size, position, and direction.

2. Problem-Solving Scenarios: The teacher presents two problem-solving scenarios that will introduce the need for the concept of symmetry and the Cartesian plane. The scenarios can be as follows:

   • Scenario 1: The teacher draws a butterfly on one side of a paper and folds it in half. Asks students what they think will happen when he unfolds the paper. This practical activity will help illustrate the concept of symmetry.
   • Scenario 2: The teacher presents a challenge: 'If I had to draw a heart on paper without looking, how could I make it symmetrical?' This will prompt students to start thinking about symmetry and the need for a tool like the Cartesian plane.

3. Contextualization: The teacher contextualizes the importance of symmetry in everyday life. He may mention that symmetry is an important property in art, nature (in many flowers, animals, and insects), and in many objects we use daily (such as the human face, a car, a house, etc.). The teacher may provide visual examples to reinforce this idea.

4. Introduction to the Topic: The teacher introduces the topic of the lesson, explaining that they will learn about symmetry and how the Cartesian plane can help them understand and identify symmetry in figures. He may say: 'Today, we will learn about a special property that some figures have. It's as if they were mirrored. When you fold the figure in half, the two parts fit perfectly. Let's find out more about this and how we can use the Cartesian plane to help'.

Development (20 - 25 minutes)

1. 'Symmetric Art' Activity

   • The teacher divides the class into small groups of 4 to 5 students and distributes blank sheets of paper and colored pencils to each group.
   • Each group is challenged to create a figure that is symmetrical. They can fold the paper in half to check if the figure is symmetrical or not.
   • The teacher circulates around the room, offering support and encouraging students to think about symmetry in their creations. He may ask questions like: 'How do you know the figure is symmetrical?' or 'Which parts of the figure are symmetrical in relation to the fold?'.
   • Once the groups have created their symmetrical figures, the teacher introduces the concept of the axis of symmetry, explaining that it is an imaginary line along which a figure can be folded to create two equal parts.

2. 'Pass the Image' Activity

   • Still in their groups, students are challenged to play the 'Pass the Image' game. The teacher draws a figure on the board that is symmetrical in relation to one of the axes of the Cartesian plane and calls out a student's name to start.
   • The student who starts must stand up and reproduce the figure drawn by the teacher on the group's paper. Then, they pass the pen to the next student, who must draw the next part of the figure, respecting the symmetry.
   • The game continues until all students in the group have had the opportunity to draw a part of the figure. The teacher may give a small prize to the group that finishes with the most symmetrical figure.

3. 'Symmetry Hunt' Activity

   • The teacher draws some figures on the board (such as a heart, a star, a triangle, etc.) and marks a point on the Cartesian plane for each figure.
   • He divides the class into groups and distributes sheets of paper with the Cartesian plane drawn for each group.
   • The groups must draw on their Cartesian plane a figure symmetrical to the figure the teacher drew on the board, respecting the marked point as the center of symmetry.
   • The teacher circulates around the room, observing the progress of the groups and offering help when needed.

These activities are designed to engage students and allow them to explore the concept of symmetry in a practical and fun way. They are flexible and can be adapted to meet the class's needs and the available time.

Feedback (10 - 15 minutes)

1. Group Discussion

   • The teacher gathers all students in a large circle and initiates a discussion about the solutions and discoveries of each group during the activities.
   • He asks a representative from each group to share the figure they created in the 'Symmetric Art' activity, explaining why they consider it symmetrical.
   • Next, the teacher asks students to share their experiences in the 'Pass the Image' game and the 'Symmetry Hunt' activity. Who was the first to notice the symmetry? Was there any difficulty in drawing the symmetrical figure?
   • During the discussion, the teacher asks questions to deepen students' understanding, such as: 'What kind of figures are easier to draw symmetrically? Why?' or 'What happens if we change the point of symmetry?'.

2. Connection to Theory

   • The teacher revisits the theoretical concepts learned in the lesson introduction and connects them to the practical activities. He reinforces the concept of symmetry and axis of symmetry, explaining how these concepts were applied in the activities.
   • The teacher also reviews the concept of the Cartesian plane, reminding students that it is a tool that helps represent and identify symmetry in figures.
   • To reinforce learning, the teacher may suggest that students write a reflection on what they learned in the lesson. He can ask questions like: 'Why is symmetry important? How can the Cartesian plane help us identify symmetry?'.

3. Final Reflection

   • The teacher concludes the lesson by asking students to reflect on what they have learned. He asks two simple questions to guide students' reflection:
     1. 'What was the most interesting thing you learned today about symmetry?'.
     2. 'How can you use what you learned today in your daily life?'.
   • Students have a minute to think about their answers to the questions. Then, the teacher may ask some students to share their answers with the class.

This final phase of the lesson is crucial as it allows the teacher to assess students' understanding of the topic and reinforce important concepts. It also encourages students to reflect on what they have learned and recognize the relevance of the content to their daily lives.

Conclusion (5 - 10 minutes)

1. Summary and Recap

   • The teacher begins the conclusion by recalling the main points covered in the lesson. He recaps the definition of symmetry, the concept of the axis of symmetry, and how the Cartesian plane can be used to represent and identify symmetry in figures.
   • He provides a brief summary of the practical activities carried out, highlighting the most important discoveries and learnings. He may ask students: 'What did you discover about symmetry today?' or 'How did you use the Cartesian plane to identify symmetry?'.

2. Connection between Theory and Practice

   • The teacher emphasizes the importance of the connection between theory and practice. He explains that by learning about symmetry, students not only acquired theoretical knowledge but also applied it practically in the activities.
   • He highlights that the practical activities helped consolidate students' theoretical understanding of symmetry and the Cartesian plane, allowing them to better understand and appreciate these concepts.

3. Extra Materials

   • The teacher suggests extra materials for students who wish to deepen their knowledge on the subject. This may include children's books that address the concept of symmetry, interactive online games involving symmetry and Cartesian planes, and educational videos available on the internet.
   • He may also suggest that students practice identifying symmetry in their environment, observing symmetry in everyday objects and drawing their own symmetrical figures at home.

4. Importance in Daily Life

   • Finally, the teacher highlights the importance of symmetry in daily life. He explains that symmetry is a fundamental concept in mathematics and art, widely used in architecture, design, painting, and other areas.
   • He emphasizes that the ability to identify and create symmetry can help students develop their spatial thinking and creativity. For example, when drawing or building something, they can use symmetry to make their creation more attractive and balanced.

5. Closure

   • To conclude the lesson, the teacher congratulates students on their work and reinforces that practice is essential to deepen understanding of the content. He encourages them to continue exploring the concept of symmetry and using the Cartesian plane in their future mathematical activities.
   • He also points out that although symmetry is a mathematical concept, it is a skill that can be applied in many aspects of their lives, from creating art to organizing objects at home.