Objectives (5 - 7 minutes)

1. Understand the concept of ratio and proportion, identifying them in everyday situations.
2. Develop skills in calculating ratios and proportions, applying them to practical problems.
3. Practice problem-solving involving the ratio between quantities, using the rule of three.

Secondary Objectives:

• Stimulate critical thinking and problem-solving skills.
• Foster the ability to contextualize mathematical content, relating it to everyday situations.
• Develop teamwork skills through practical group activities.

Introduction (10 - 15 minutes)

1. Review of Previous Content: The teacher starts the lesson by reviewing the concepts of quantities, units of measurement, and proportions, which are essential for understanding the topic of ratio. This can be done through a brief theoretical review or through a question and answer game to engage the students. (3 - 5 minutes)

2. Problem Situations: Next, the teacher presents two problem situations that involve the calculation of ratios. For example, "If a cake recipe calls for 2 cups of flour to 1 cup of milk, what is the ratio between the amount of flour and the amount of milk?" and "If a car travels 200 km in 4 hours, what is the ratio between the distance traveled and the time taken?" These situations will serve as a starting point for introducing the concept of ratio. (3 - 5 minutes)

3. Theme Contextualization: The teacher then contextualizes the importance of the concept of ratio, showing how it is applied in various areas of knowledge and everyday life. For example, in engineering to calculate the proportion of materials in a construction, in cooking to adjust the quantities of ingredients in a recipe, or in economics to calculate the return on an investment. (2 - 3 minutes)

4. Topic Introduction: Finally, the teacher introduces the topic of ratio, explaining that it is the comparison between two or more quantities of the same nature. They can use simple examples, such as the ratio between the height of two students, the ratio between the number of boys and girls in a classroom, or the ratio between the number of school days and holidays. The teacher can also show the mathematical notation for the ratio, using the symbol ":" or the fraction bar. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Activity 1 - "Ratio in the Kitchen" (10 - 12 minutes)

   • Description: The teacher divides the class into groups of 4 to 5 students and gives each group a cake recipe. The recipes should have ingredient quantities doubled, tripled, and quadrupled in relation to the amount of a single cake. The challenge is to calculate the ratio between the quantity of each ingredient and the number of cakes the recipe makes.
   • Step by Step:
     1. The teacher guides the students to read the recipe and identify the ingredients and their respective quantities.
     2. Next, the students must calculate the ratio between the quantity of each ingredient and the number of cakes the recipe makes.
     3. Finally, the students should compare the calculated ratios for the recipes that double, triple, and quadruple the number of cakes, and verify if they are equal.

2. Activity 2 - "Ratio in Traffic" (10 - 12 minutes)

   • Description: The teacher proposes a challenge of problem-solving involving the ratio between distance and time. They present to the students the situation of a car that travels a certain distance in a time x, and ask them to calculate the time it would take for the car to travel the same distance if it were traveling at twice the speed.
   • Step by Step:
     1. The teacher guides the students to identify the data of the problem: the distance and the time.
     2. Next, the students must calculate the ratio between the distance and the time.
     3. Finally, the students should use the rule of three to calculate the time it would take for the car to travel the same distance if it were traveling at twice the speed.

3. Activity 3 - "Ratio in Everyday Life" (5 - 7 minutes)

   • Description: The teacher asks the students to think of other everyday situations where the ratio is used. Each group should write down at least three situations and explain how the ratio is applied in each of them. In the end, each group must present their situations to the class.
   • Step by Step:
     1. The teacher guides the students to think of situations in everyday life where the ratio is used.
     2. Each group should write down their situations and explain how the ratio is applied.
     3. Finally, each group must present their situations to the class.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes)

   • The teacher invites each group to share their solutions or conclusions from the activities carried out. Each group will have up to 3 minutes to present.
   • During the presentations, the teacher should encourage other students to ask questions and make comments to promote discussion and sharing of ideas.

2. Connection to Theory (2 - 3 minutes)

   • After all the presentations, the teacher should summarize the main ideas presented, connecting them to the theory. For example, they can emphasize how students applied the concept of ratio and proportion to solve the problems presented.
   • The teacher can also take this opportunity to clarify any remaining doubts and reinforce the key concepts of the lesson.

3. Individual Reflection (2 - 3 minutes)

   • The teacher suggests that students reflect individually on what they learned in the lesson. They ask guiding questions, such as: "What was the most important concept you learned today?" and "What questions have not been answered yet?".
   • Students will have a minute to think about their answers. The teacher may ask some students to share their reflections with the class, if they wish.

4. Teacher Feedback (1 minute)

   • Finally, the teacher gives overall feedback on the lesson, reinforcing the positive points and indicating areas where students may need to review or practice more. They may also give a preview of what will be covered in the next lesson, to keep students motivated and engaged.
   • The teacher concludes the lesson, thanking everyone for their participation and encouraging them to continue studying and practicing the content at home.

Conclusion (5 - 7 minutes)

1. Lesson Summary (2 - 3 minutes)

   • The teacher should start the Conclusion by summarizing the main points covered in the lesson. This includes the definition of ratio and proportion, the mathematical notation for ratio, problem-solving involving the ratio between quantities, and the application of the rule of three.
   • This can be done interactively, asking students to recall the concepts or explain them in their own words.

2. Theory-Practice Connection (1 - 2 minutes)

   • Next, the teacher should highlight how the lesson connected theory with practice, using the activities carried out to illustrate the application of theoretical concepts.
   • They can reinforce that Mathematics is not just a theoretical discipline, but a practical tool that can be used to solve everyday problems.

3. Extra Materials (1 minute)

   • The teacher can suggest extra materials for students who wish to deepen their knowledge on the topic. This may include Mathematics books, educational websites, explanatory videos on YouTube, or Mathematics learning apps.
   • They can also recommend practice exercises, so that students can consolidate what they learned in the lesson.

4. Importance of the Topic (1 - 2 minutes)

   • Finally, the teacher should emphasize the importance of the topic of ratio for everyday life and other disciplines. They can give examples of how ratio is used in different contexts, such as in cooking, engineering, economics, or science.
   • They can also encourage students to be attentive to everyday situations where ratio can be used, as a way to reinforce learning and the applicability of the concept.