Objectives (5 - 7 minutes)

1. Understand the concept of translation on the Cartesian plane: Students should be able to understand what a translation is, how it works, and how it is represented on the Cartesian plane. This includes understanding the movement of an object or figure without altering its size or shape.

2. Identify the properties of translations and how they apply on the Cartesian plane: Students should be able to identify the characteristics of a translation, such as direction, sense, and distance, and how they are represented on the Cartesian plane. This includes understanding how the properties of a translation affect the position of an object or figure.

3. Solve practical problems involving translations on the Cartesian plane: Students should be able to apply the acquired knowledge to solve practical problems involving translations on the Cartesian plane. This includes the ability to determine the final position of an object or figure after a series of translations.

Secondary Objectives:

• Develop logical and spatial reasoning skills: Through the study of translations on the Cartesian plane, students will be encouraged to develop logical and spatial reasoning skills, which can be useful in other areas of mathematics and beyond.

• Foster collaboration and discussion in the classroom: The activities proposed for the practical lesson aim to foster collaboration among students, encouraging discussion and the exchange of ideas. This interaction can strengthen learning, allowing students to see different perspectives and approaches to problem-solving.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher should start the lesson by reviewing the concepts of Cartesian coordinates and the representation of points and figures on the Cartesian plane. This can be done through a brief recap of previous topics or a quick quiz to assess students' understanding.

2. Problem situation: The teacher can present two problem situations involving translations on the Cartesian plane to spark students' interest. For example, "How can we move a figure on the plane without altering its size or shape?" and "If we have the figure of a plane flying from point A to point B on the plane, how can we represent this movement as a translation?".

3. Contextualization: The teacher should then explain the importance of translations on the Cartesian plane, highlighting how they are used in various areas, such as in physics to represent the movement of objects, in computer graphics for animations and games, and even in art and design to create patterns and symmetries.

4. Introduction of the topic: To introduce the topic of translations on the Cartesian plane, the teacher can share some interesting facts or applications. For example, he can mention how the concept of translation is used to describe the movement of planets around the sun, or how artists use translations to create repetitive patterns in their works.

5. Capture students' attention: To capture students' attention, the teacher can share some curiosities or stories related to the topic. For example, he can mention that the term "translation" comes from the Latin "translatio," which means "to move from one place to another," or he can tell the story of how the French mathematician René Descartes created the Cartesian coordinate system in the 17th century, which is the basis for the study of translations on the Cartesian plane. Additionally, the teacher can show some images or videos of practical examples of translations, such as a flying plane or a moving car on a road.

Development (20 - 25 minutes)

1. Activity "Translation of a city": The teacher will divide the class into groups of 4 to 5 students and provide each group with a map of a fictional city drawn on the Cartesian plane. Students will be tasked with "moving" a building from one location to another through a series of translations. The teacher will provide the initial and final coordinates of the building, and students will need to determine the coordinates of each step of the translation. Students will need to apply the properties of translations (direction, sense, and distance) to complete the task. At the end of the activity, each group will present their map and explain how they performed the translations. (10 - 12 minutes)

   • Materials needed: City maps, colored markers, ruler, graph paper.

2. Activity "Translation Puzzle": The teacher will provide each group of students with a puzzle composed of several pieces. Each piece of the puzzle will have a figure drawn on the Cartesian plane. Students will be tasked with "assembling" the puzzle by moving the pieces through translations. Each piece will have a set of instructions (for example, "move 3 units to the right and 2 units up") that students must follow to complete the puzzle. This activity will allow students to practice applying the properties of translations in a playful and challenging way. (8 - 10 minutes)

   • Materials needed: Translation puzzles, stopwatch.

3. Activity "Translation Game": This activity aims to reinforce learning in a playful and competitive way. The teacher will divide the class into two teams and provide each team with a set of cards. Each card will have a figure drawn on the Cartesian plane and a set of instructions to perform a translation. One member of each team at a time must pick a card, follow the instructions, and place the resulting figure on the Cartesian plane. The team that can correctly place the highest number of figures on the Cartesian plane within a set period of time will be the winner. (5 - 7 minutes)

   • Materials needed: Cards with figures and translation instructions, stopwatch.

Throughout all activities, the teacher should circulate around the room, monitoring the progress of the groups, clarifying doubts, and encouraging discussion and logical reasoning.

Return (8 - 10 minutes)

1. Group discussion (3 - 4 minutes): After the conclusion of the activities, the teacher should lead a group discussion, giving each group the opportunity to share their solutions or conclusions. During this discussion, the teacher should encourage students to explain the reasoning behind their answers, highlighting the application of the properties of translations on the Cartesian plane. The teacher should also point out the connections between the solutions of different groups, highlighting different approaches to the same problem.

2. Connection to theory (2 - 3 minutes): The teacher should then connect the practical activities carried out with the theory discussed in the Introduction of the lesson. This can be done through questions like: "How are translations represented on the Cartesian plane?" or "How were the properties of translations applied to move the figures in the puzzle or on the city map?". The goal is for students to realize the relevance and usefulness of theory in solving practical problems.

3. Individual reflection (2 - 3 minutes): To consolidate learning, the teacher should propose a moment of individual reflection. Students should think for a minute about the following questions: "What was the most important concept learned today?" and "What questions have not been answered yet?". After the minute of reflection, the teacher can ask some students to share their answers, promoting an environment of respect and appreciation for different perceptions and learnings.

4. Feedback and clarification of doubts (1 minute): Finally, the teacher should request feedback from students about the lesson, asking what they liked most and what they would have liked to learn differently. Additionally, the teacher should clarify any doubts that may still exist, ensuring that all students have understood the lesson content.

Throughout the Return, the teacher should pay attention to students' participation, encouraging the expression of ideas and the formulation of questions. The goal is for students to feel comfortable sharing their doubts and reflections, promoting a collaborative and inclusive learning environment.

Conclusion (5 - 7 minutes)

1. Summary of contents (2 - 3 minutes): The teacher should start the Conclusion of the lesson by summarizing the main points covered. This includes the definition of translations on the Cartesian plane, the properties of translations (direction, sense, and distance), and how they are represented on the Cartesian plane. The teacher can recall the answers to the problem situations presented at the beginning of the lesson, highlighting how the knowledge about translations was applied to solve them. Additionally, the teacher should reinforce the importance of developing logical and spatial reasoning skills, which were stimulated during the practical activities.

2. Connection between theory and practice (1 - 2 minutes): Next, the teacher should explain how the lesson connected theory to practice. This can be done by highlighting how the practical activities allowed students to apply and experience the theoretical concepts discussed. The teacher can also mention how group discussions and individual reflection served to deepen students' understanding of the topic.

3. Extra materials (1 minute): To complement learning, the teacher can suggest some extra materials for students to explore. This may include educational videos about translations on the Cartesian plane, online exercises to practice solving problems involving translations, or interactive games that use the concept of translation. The teacher can also indicate sections of textbooks or math websites that address the topic in more detail.

4. Importance of the subject in everyday life (1 minute): Finally, the teacher should emphasize the importance of translations on the Cartesian plane in everyday life. The teacher can mention examples of how understanding this concept can be useful in various situations, such as in solving navigation problems, designing objects, or understanding physical phenomena. Additionally, the teacher can highlight how developing logical and spatial reasoning skills can be beneficial not only in mathematics but in many other areas of life.