Objectives (5 - 7 minutes)

1. Introducing the concept of Cartesian Coordinates: The teacher should explain in a clear and simple way what Cartesian coordinates are and how they are used to locate points on a plane. It should be emphasized that a point on the plane is represented by an ordered pair (x, y) where x is the horizontal coordinate and y is the vertical coordinate.

2. Teaching how to locate points on a plane using Cartesian coordinates: The teacher should ensure that students understand how to locate a point on a plane from an ordered pair, following the steps: (1) move horizontally (x positions) from the origin (0, 0) and (2) move vertically (y positions) from the new position.

3. Providing practical activities for the application of the concept: The teacher should plan fun and interactive activities that allow students to apply what they have learned about Cartesian coordinates. These activities should be designed to be suitable for the students' level of development, while challenging them to think critically and solve problems.

At the end of this stage, students should be able to understand what Cartesian coordinates are, how they are used to locate points on a plane, and be able to apply this knowledge to solve problems in a practical and playful way.

Introduction (10 - 12 minutes)

1. Review of previous content: The teacher starts the lesson by quickly reviewing previously studied mathematical concepts, such as ordinal and cardinal numbers, basic geometric shapes (circle, square, triangle), and directions (left, right, up, down). This review serves to prepare the ground for the introduction of the new concept of Cartesian coordinates.

2. Problem-solving situations: The teacher presents two simple but challenging situations that can be easily solved using Cartesian coordinates. For example:

   • Situation 1: "Imagine you are in a game room and want to find the exact position of a toy on a large map. How would you describe the toy's position to a friend on the other side of the room?"
   • Situation 2: "You are in a park and want to find the exact location where you hid a treasure box for your friends to find. How can you describe the location to them using only words?"

3. Contextualization of the subject's importance: The teacher explains that Cartesian coordinates are an important tool used not only in Mathematics but also in many other areas, such as Geography, Computer Science, and even GPS. The teacher can say:

   • "Do you know that car and cellphone navigators use coordinates to guide us to a destination, right? This is possible thanks to Cartesian coordinates. Coordinates are also used to map lands, locate lost people, and even to draw characters in computer games!"

4. Introduction of the topic: The teacher introduces the topic of the lesson, Cartesian coordinates, explaining that it is a way to describe the exact location of a point on a plane. To make the introduction more interesting, the teacher can tell the story of René Descartes, the French mathematician and philosopher who invented this coordinate system. The teacher can share curiosities, such as the fact that Descartes invented Cartesian coordinates while he was in bed, sick, and watched flies flying on the ceiling!

5. Capturing students' attention: The teacher proposes two "curiosities" to instigate students' curiosity and interest in the subject:

   • Curiosity 1: "Did you know that Cartesian coordinates can be used to draw images? Yes, it's true! This is called fractal art and is widely used in computer graphics."
   • Curiosity 2: "What if I told you that with Cartesian coordinates you can draw a heart? Would you be surprised? At the end of the lesson, I will show you how this is possible!"

At the end of this stage, students should be excited and ready to learn more about Cartesian coordinates.

Development (20 - 25 minutes)

During the development stage, the teacher will present three practical activities to consolidate students' learning about Cartesian coordinates. The choice of which activity will be carried out will depend on the students' level of understanding and development.

Activity 1: "Coordinates Maze"

1. The teacher should draw a large maze on the classroom floor, marking the paths with adhesive tape. At the end of the maze, the teacher should draw a "treasure" (an object or figure that students like).
2. Each student, or group of students, receives a pair of dice (or a large die with numbers from 1 to 6 written on each face). They must roll the die and move in the maze in the direction corresponding to the result of the die. For example, if they roll a 4, they must move 4 spaces to the right.
3. The students' goal is to find the "treasure" in the fewest possible rolls. To do this, they must discuss and decide together the best strategy to move through the maze, considering Cartesian coordinates.

Activity 2: "Treasure Hunt"

1. The teacher should hide several "treasures" (small objects or figures) around the classroom, each with a coordinate written on a card placed next to it.
2. Students, individually or in groups, receive a worksheet with a grid of Cartesian coordinates (x, y) and must write down the coordinates of each "treasure" they find.
3. The goal is to collect as many "treasures" as possible and record the coordinate of each one. In the end, students should share their findings and compare their worksheets, checking if all the "treasures" were found.

Activity 3: "Drawing with Coordinates"

1. The teacher should divide the students into pairs. Each pair receives a gridded paper and colored pencils.
2. The teacher should give the students a series of coordinates (for example, (2, 3), (4, 1), (-1, 5), etc.) and the students, working together, must mark these coordinates on the paper.
3. After marking all the coordinates, the students connect the dots with straight lines, creating a drawing. In the end, they will have drawn a surprise object (for example, a heart, a star, an animal, etc.).

The teacher should choose the activity that best suits the pace and level of understanding of the students. It is important for the teacher to circulate around the classroom during the activities, observing the students' progress, answering questions, and promoting interaction among them.

Discussion (8 - 10 minutes)

1. Group discussion: After completing the activities, the teacher should gather all students in a large circle to promote a group discussion. Each group should present their answers, solutions, and strategies used during the activities.

2. Verification of answers: The teacher should then verify the answers and solutions presented by the students. During this verification, the teacher should highlight the most creative solutions, the most efficient strategies, and the most common errors, ensuring that all students have a clear understanding of the content.

3. Connection with theory: After the verification, the teacher should ask questions to help students connect theory with practical activities. For example, the teacher can ask: "How did you use Cartesian coordinates to move in the maze?" or "How did you use Cartesian coordinates to find the 'treasures' in the classroom?"

4. Final reflection: To conclude the discussion, the teacher should propose that students reflect for a minute on what they learned in the lesson. The teacher can ask two simple questions to guide this reflection:

   • Question 1: "Can you think of a situation where you could use Cartesian coordinates outside the classroom?"
   • Question 2: "What did you find most interesting about Cartesian coordinates?"

5. Teacher's feedback: The teacher should praise the students' efforts during the lesson, emphasizing the importance of teamwork, creativity, and the practical application of mathematical concepts. The teacher should also reinforce the most important points of the lesson, briefly reviewing the concepts of Cartesian coordinates and their application in locating points on a plane.

At the end of this stage, students should have a clear understanding of the concept of Cartesian coordinates, have practiced applying this concept in real situations, and have been able to connect theory with practice.

Return (5 - 8 minutes)

1. Lesson Summary: The teacher should start the return stage by summarizing the main points covered during the lesson. This includes the definition of Cartesian coordinates, the way to locate points on a plane using coordinates, and the practical applications of the concept. The teacher can ask for students' help to remember these points, encouraging them to share what they have learned with the class.

2. Connection between Theory and Practice: Next, the teacher should reinforce the connection between the presented theory and the practical activities carried out. The teacher can highlight how the activities "Coordinates Maze," "Treasure Hunt," and "Drawing with Coordinates" allowed students to apply theoretical concepts in a fun and meaningful way.

3. Reflection on the Importance of the Subject: The teacher should propose that students reflect on the importance of Cartesian coordinates. For this, the teacher can ask two simple questions:

   • Question 1: "How can Cartesian coordinates help you locate yourself in an unknown place, like a park or a mall?"
   • Question 2: "In what other situations do you think you could use Cartesian coordinates?"

4. Addressing Possible Doubts: The teacher should take time to address any doubts that may have arisen during the lesson. The teacher can ask students if there is anything they still do not fully understand and explain the necessary points again in a clear and simple way.

5. Extra Materials: To complement learning, the teacher can suggest some extra materials for students to explore at home. This may include math books with sections on Cartesian coordinates, online games involving the use of coordinates, and educational videos available on the internet. The teacher can also suggest that students practice drawing with coordinates at home, creating their own drawings and sharing them with the class in the next lesson.

6. Students' Feedback: Finally, the teacher should ask students for feedback on the lesson. The teacher can ask two simple questions to get this feedback:

   • Question 1: "What did you like most about today's lesson?"
   • Question 2: "What do you think we could do differently next time to make the lesson even more interesting?"

At the end of this stage, students should have consolidated their understanding of Cartesian coordinates, be aware of the importance and applications of the concept, and be engaged and motivated to learn more about the subject.

Conclusion (3 - 5 minutes)

1. Lesson Summary: The teacher should conclude the lesson by summarizing the main points covered. This includes the definition of Cartesian coordinates, the way to locate points on a plane using coordinates, and the practical applications of the concept. The teacher can recall the examples of problem-solving situations presented at the beginning of the lesson and how students were able to solve them using Cartesian coordinates.

2. Connection between Theory and Practice: The teacher should emphasize how the lesson connected theory and practice, allowing students to apply theoretical concepts in a fun and meaningful way. The teacher can say: "Today, you not only learned about Cartesian coordinates but also used them to solve real problems and even to draw! This shows how Mathematics can be useful and fun at the same time."

3. Extra Materials: The teacher should reinforce the importance of continuing to learn about the subject at home. To do this, the teacher can suggest some extra materials again, such as math books, online games, and educational videos. The teacher can say: "I encourage all of you to explore more about Cartesian coordinates at home. There are many resources available, and I'm sure you will have even more fun with this subject!"

4. Importance of the Subject: The teacher should remind students of the importance of the subject in their daily lives. It can say: "Remember that Cartesian coordinates are not just an abstract mathematical concept, but a very useful tool. They are used to describe the location of objects on maps, to navigate using GPS, and even to draw images in computer games!"

5. Final Curiosities: To end the lesson in a playful and interesting way, the teacher can share two final curiosities about the subject.

   • Curiosity 1: "Did you know that the name 'Cartesian coordinates' comes from the mathematician and philosopher René Descartes, who invented them?"
   • Curiosity 2: "And did you know that Cartesian coordinates can be used to draw amazing images? If you want, in the next lesson, I can show you how to draw a heart using coordinates!"

At the end of this stage, students should have a clear and consolidated understanding of the concept of Cartesian coordinates, as well as be motivated and excited to explore more about the subject.