Objectives (5 - 7 minutes)

• Understand the concept of Rotations in the Cartesian Plane: Students should be able to understand what a rotation in the Cartesian plane means, how it is performed, and what it does to the object or figure being rotated.

• Identify the Rotation of Geometric Figures in the Cartesian Plane: Students should be able to identify and describe how a geometric figure is altered in a rotation in the Cartesian plane. They should be able to apply this to different figures, including squares, rectangles, triangles, and circles.

• Calculate the Coordinates of a Rotated Figure in the Cartesian Plane: Students should be able to calculate the new coordinates of a figure after a rotation in the Cartesian plane. This involves understanding how the x and y coordinates are affected by the rotation.

Introduction (10 - 15 minutes)

• Review of previous concepts: The teacher should start the lesson by reviewing the concepts of coordinates in the Cartesian plane, angles, and geometric transformations (translation and reflection). These concepts are fundamental to understanding rotations in the Cartesian plane. (3 - 5 minutes)

• Problem-solving situations: The teacher can present two problem-solving situations to arouse students' interest and contextualize the lesson topic. For example:

  1. "Imagine you are playing with a stencil of a triangle in the Cartesian plane and decide to rotate it 90 degrees clockwise. Where will the new triangle be on the Cartesian plane?"

  2. "Now, if you rotate the triangle 180 degrees counterclockwise, what happens? Where will the triangle be now?" (5 - 7 minutes)

• Contextualization of the importance of the subject: The teacher should explain how rotations in the Cartesian plane are used in practice, whether in digital drawings and graphics, computer games, engineering, architecture, among others. (2 - 3 minutes)

• Introduction to the topic: To capture students' attention, the teacher can introduce the topic with some curiosities:

  1. "Did you know that most computer games and animations in movies use rotations in the Cartesian plane to move characters and objects?"

  2. "And that rotating an object in 3D space is essential for virtual and augmented reality, allowing you to see the object from different angles?" (3 - 5 minutes)

Development (20 - 25 minutes)

• Activity 1: Clockwise Rotation (10 - 12 minutes)

  • Description: In this activity, students will use a drawing of a clock in the Cartesian plane to understand rotation. They will be asked to rotate the clock's "hours" at different angles and record the new positions on the Cartesian plane. This will help students visualize how rotation affects the coordinates of an object.

  • Step by step:

    1. The teacher should provide each student with a drawing of a clock in the Cartesian plane, with the "hours" (which are triangles) in the initial position (12, 3, 6, and 9 o'clock).
    2. The teacher should explain that the task is to rotate the clock's "hours" at different angles (e.g., 30, 60, 90 degrees) and record the new positions on the Cartesian plane.
    3. Students should rotate the paper with the clock to visualize the rotation and then trace the new triangle on the Cartesian plane.
    4. Students should repeat the process for different rotation angles.
    5. After completing the activity, students should discuss their observations and conclusions in a short classroom debate.

• Activity 2: Drawing with Rotation (10 - 12 minutes)

  • Description: In this activity, students will use vector drawing software (such as Inkscape or Adobe Illustrator) to create and rotate their own figures in the Cartesian plane. This activity will allow students to apply the concept of rotation in a more practical and fun way.

  • Step by step:

    1. The teacher should organize students into groups and provide each group with a laptop with the vector drawing software open.
    2. The teacher should explain that the task is to create a simple figure (such as a triangle, square, rectangle, etc.) in the Cartesian plane of the software.
    3. Then, students should rotate the figure at different angles (using the software's rotation tool) and observe how the figure's coordinates change.
    4. Students should repeat the process for different figures and rotation angles.
    5. After completing the activity, students should present their rotated figures to the class and explain the process they used.

The teacher should circulate around the room, providing guidance and clarifying doubts as necessary. At the end of the activities, the teacher should gather the class for a group discussion, where students can share their observations, difficulties, and learnings.

Return (8 - 10 minutes)

• Group discussion (3 - 4 minutes): The teacher should gather all students and promote a group discussion on the solutions or conclusions found by each team during the activities. This will allow students to share their experiences, learn from each other, and reinforce what was learned.

• Connection with theory (3 - 4 minutes): The teacher should then make the connection between the activities carried out and the theory discussed in the Introduction of the lesson. It should be highlighted how the understanding of rotations in the Cartesian plane is applied in practice, especially in fields such as engineering, architecture, and computer graphics.

• Individual reflection (2 - 3 minutes): To conclude the lesson, the teacher should propose that students reflect individually on what they have learned. Some questions that can be asked include:

  1. "What was the most important concept you learned today about rotations in the Cartesian plane?"
  2. "Were you able to solve the problem-solving situations we presented at the beginning of the lesson? If yes, how? If not, what was the difficulty?"
  3. "How do you think rotations in the Cartesian plane can be useful in your daily life or future career?"

The teacher should encourage students to write down their answers and, if possible, share them in the next lesson. This reflection will help students consolidate what they have learned and prepare for future topics. Additionally, student feedback will be valuable for the teacher to assess the effectiveness of the lesson and make adjustments if necessary.

Conclusion (5 - 7 minutes)

• Lesson Summary (2 - 3 minutes): The teacher should summarize the main points discussed in the lesson, reinforcing the concept of rotations in the Cartesian plane, the identification of rotations of geometric figures, and the calculation of the coordinates of a rotated figure. The teacher can use a whiteboard or a slide presentation to visualize and reinforce the concepts, if necessary.

• Connection between Theory and Practice (1 - 2 minutes): The teacher should highlight how the practical activities carried out in the lesson helped illustrate and deepen the understanding of the theoretical concepts presented. This may include a discussion on how the "Clockwise Rotation" activity helped visualize the rotation of figures in the Cartesian plane and how the "Drawing with Rotation" activity allowed students to apply these concepts in a practical and fun scenario.

• Extra Materials (1 - 2 minutes): The teacher should suggest extra materials for students who wish to deepen their knowledge of rotations in the Cartesian plane. This may include math books, educational websites with tutorials and interactive exercises, explanatory videos on YouTube, among others. The teacher can share these resources through an online learning platform, such as a school website or a study group.

• Importance of the Subject (1 - 2 minutes): Finally, the teacher should emphasize the importance of rotations in the Cartesian plane in everyday life and in various application areas. It can be mentioned how these concepts are used in fields such as computer graphics, engineering, architecture, physics, among others. The teacher can encourage students to think about everyday situations or their future careers where understanding rotations in the Cartesian plane can be useful.