Objectives (5 - 10 minutes)

1. Understand the concept of ratio: Students should be able to understand what a ratio is and how it represents the relationship between two quantities. They should be able to identify ratios in everyday situations and in simple mathematical problems.

2. Apply the concept of ratio in problems: Students should be able to apply the concept of ratio to solve problems. They should be able to identify the quantities given in the proportion, find the ratio between them, and use this ratio to determine the unknown quantity.

3. Introduction to the concept of proportion: Students should be introduced to the concept of proportion as an equality of two ratios. They should understand that proportions can be used to compare two or more quantities in a simple and direct way.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher should start the lesson by reminding students of mathematical concepts that are fundamental to understanding ratios and proportions, such as addition, subtraction, multiplication, and division. This review can be done interactively, through questions and answers, or with the help of manipulative materials, such as building blocks or counting chips. The teacher can propose simple problem situations involving these operations so that students can apply their knowledge.

2. Contextualization of the subject's importance: The teacher should then explain to students why learning about ratios and proportions is important. He can mention everyday situations where these concepts are used, such as adjusting ingredient quantities when baking a cake, or calculating the price of a product on sale. The teacher can also mention how these concepts are applied in other subjects, such as science and geography, and in professions like engineering and architecture.

3. Introduction to the topic: The teacher should then introduce the topic of the lesson, ratios and proportions, in an interesting and engaging way for students. For example, he can propose a mathematical challenge involving the comparison of quantities, such as 'If we have 10 candies and 5 children, how many candies will each child receive?'. Then, the teacher can explain that to solve this problem, we need to use the concept of ratio, which is the comparison between two quantities.

4. Capturing students' attention: To spark students' interest, the teacher can share some curiosities about ratios and proportions. For example, he can mention that many artists use proportions to draw human bodies or build buildings. He can also mention that nature uses proportions in many of its projects, such as the way leaves are arranged on a stem or how the petals of a flower are organized.

Development (20 - 25 minutes)

1. Ratio and Proportion Verification Activity - 'The Cookie Factory': The teacher should divide the class into groups of up to 5 students. Each group will receive a 'Cookie Factory Worksheet', which presents a problem situation involving ratio and proportion. The situation is: 'The Cookie Factory produced 240 cookies and packaged them in bags of 12 cookies each. How many cookie bags were produced?'.

   The teacher should guide the students to read the situation together and discuss the best way to solve it, using the concept of ratio and proportion. They can draw or write the steps of the process to facilitate visualization. The teacher should circulate around the room, assisting the groups as needed.

   After the groups have solved the problem, the teacher should ask a representative from each group to present the solution to the class, explaining the steps they used to solve the problem. The teacher should then reinforce the concepts of ratio and proportion, relating them to the solution presented by the students.

2. Playful Ratio and Proportion Activity - 'The Lost Treasure': The teacher should propose a board game called 'The Lost Treasure', in which students use the concept of ratio and proportion to advance on the board and find the treasure.

   The board should be drawn on the board, with different colored and numbered spaces. In each space, there will be a problem for the students to solve. The problems should vary in difficulty, with some involving only ratio and others involving proportion. For each problem solved correctly, the student advances on the board.

   The teacher should divide the class into groups and distribute the game pieces to each group. They will play in rounds, with a representative from each group solving one problem at a time. The teacher should guide the students to use the strategy of ratio and proportion to solve the problems. In the end, the group that reaches the treasure first will be the winner.

   During the game, the teacher should circulate around the room, assisting the students and reinforcing the concepts of ratio and proportion. At the end of the game, the teacher should gather the class for a discussion about the strategies used and the difficulties encountered, relating them to the concepts of ratio and proportion.

3. Art Activity with Ratio and Proportion - 'The Proportional Gallery': To exercise the concept of proportion in a more playful and creative way, the teacher can propose an art activity called 'The Proportional Gallery'.

   Each group of students will receive a large sheet of paper and several old magazines. They will have to cut out images of people, animals, objects, etc. and paste them on the paper, creating an 'art gallery'. The task is to make the images in the gallery proportional to each other, according to what they learned about proportion.

   The teacher should guide the students to think about how they can use proportion to organize the images on the paper. He should remind the students that proportion means that things are 'the right size' in relation to each other. The teacher should circulate around the room, assisting the groups as needed and reinforcing the concepts of ratio and proportion.

   At the end of the activity, each group should present their 'Proportional Gallery' to the class, explaining how they used proportion to organize the images. The teacher should then reinforce the concepts of ratio and proportion, relating them to the solutions presented by the students.

These are just suggestions for activities, and the teacher can choose the one that best suits his class. Always remembering that the goal is to make learning about ratios and proportions meaningful and fun for the students.

Return (10 - 15 minutes)

1. Group Discussion: After completing the activities, the teacher should gather all students for a large group discussion. Each group will have the opportunity to share their discoveries, solutions, and strategies used during the activities. The teacher should encourage all students to participate actively, asking questions, offering comments, and expressing their opinions. During the discussion, the teacher should reinforce the concepts of ratio and proportion, connecting them to the solutions and strategies presented by the students. He should also highlight any common errors or difficulties that arose during the activities, and clarify these points if necessary.

2. Connection to Theory: After the discussion, the teacher should guide the students to reflect on how the activities connect with the theory learned at the beginning of the lesson. He can ask questions like: 'How did you use ratio and proportion to solve the problems in the 'Cookie Factory'?', 'How did you apply ratio and proportion during the game 'The Lost Treasure'?' and 'How did you use proportion in the art activity 'The Proportional Gallery'?'. Students should be able to clearly identify how they used the concepts of ratio and proportion in the different activities, and how these concepts are applied in practice.

3. Final Reflection: To conclude the lesson, the teacher should propose that students make a brief reflection on what they have learned. He can ask two simple questions to guide this reflection: 'What did you find most interesting about ratio and proportion?' and 'How can you use what you learned today in your lives outside of school?'. Students should be encouraged to share their answers with the rest of the class, promoting a collaborative and respectful learning environment.

4. Learning Assessment: During the group discussion and final reflection, the teacher should carefully observe the students' responses and comments, informally assessing the level of understanding and engagement of each one. This assessment can be used to plan future lessons and activities, adapting them to the needs and interests of the students.

5. Closure: To conclude the lesson, the teacher should reinforce the main points covered during the lesson and thank the participation and effort of all students. He should remind the students that what they learned about ratios and proportions is very important and useful, and that they will have the opportunity to apply these concepts in many everyday situations and in future math classes.

Conclusion (5 - 10 minutes)

1. Summary of key points: The teacher should start the conclusion by recalling the main points covered in the lesson. He should recap the concept of ratio and proportion, highlighting how they are used to compare and relate quantities. The teacher should also reinforce the idea that ratio is a comparison between two quantities, while proportion is an equality of two ratios. He can use practical examples and solutions to problems discussed during the lesson to illustrate these concepts.

2. Connection between theory, practice, and applications: Next, the teacher should explain how the lesson connected the theory, practice, and applications of the concepts of ratio and proportion. He can highlight how the practical activities allowed students to apply the theory in real and creative situations. Additionally, he can mention how the discussions and reflections helped solidify students' understanding of the concepts and their applications.

3. Additional Materials: To complement students' learning, the teacher can suggest some extra materials. This may include textbooks, educational websites, online games, math apps, and explanatory videos. The materials should be selected based on the needs and interests of the class, and the teacher should encourage students to explore them at home to deepen their understanding of ratios and proportions.

4. Importance of the subject: Finally, the teacher should reinforce the importance of what students have learned about ratios and proportions. He can mention how these concepts are used in various areas of life, from cooking to architecture. Additionally, he can explain how understanding ratios and proportions can help students solve math problems more efficiently and better understand the world around them.

5. Closure: To conclude the lesson, the teacher should thank the participation and effort of all students and encourage them to continue exploring and learning about ratios and proportions. He should reaffirm that everyone is capable of understanding and applying these concepts, and that practice and perseverance are essential for success in mathematics.