Objectives (5 minutes)

1. Understand the concept of area of a rectangle and parallelogram: Students should be able to define what area is and how it is calculated for rectangles and parallelograms. They should understand the meaning of a square unit and how it is used to measure the area of a figure.

2. Apply the formula for the area of a rectangle and parallelogram in real-world problems: Students should be able to use the area formula to find the area of rectangles and parallelograms in practical situations. This includes the ability to identify the appropriate measurements in the figure and substitute them into the formula.

3. Differentiate rectangles from parallelograms and identify their properties: Students should be able to distinguish between rectangles and parallelograms based on their characteristics, such as sides and angles. This allows them to correctly apply the area formula and solve problems involving these figures.

   Secondary Objectives:

   • Develop critical thinking and problem-solving skills: By solving problems involving the area of rectangles and parallelograms, students will be challenged to think critically and apply their mathematical skills to find solutions.

   • Promote teamwork and collaboration: The inverted classroom is a great opportunity to promote teamwork and collaboration among students. They can discuss concepts and problems together, assisting each other in understanding and solving them.

Introduction (10 - 15 minutes)

1. Review of previous concepts - The teacher should start the lesson by reviewing the concepts of perimeter and area that were previously covered. This review can be done interactively, asking students to share their definitions and examples. (3 - 5 minutes)

2. Problem situation 1 - After the review, the teacher can present the following situation: "Imagine you are designing the floor of a rectangular room. You need to calculate the number of tiles needed to cover the floor. How would you do that?" This situation serves to contextualize the concept of area and prepare students for the lesson topic. (2 - 3 minutes)

3. Contextualization of the topic's importance - The teacher should then emphasize the importance of calculating area in everyday life. They can mention examples such as calculating the area of a plot of land, calculating the area of a painting to determine the amount of paint needed, among others. (1 - 2 minutes)

4. Curiosity 1 - To spark students' interest, the teacher can share the following curiosity: "Did you know that the formula for calculating the area of a rectangle (base x height) is the same for calculating the area of a parallelogram? This is because a parallelogram is actually a rectangle that has been 'stretched' or 'compressed' on one side." (1 - 2 minutes)

5. Curiosity 2 - Another curiosity that can be shared is: "Did you know that the area of a rectangle is always greater than its perimeter, but the area of a parallelogram can be smaller, equal, or greater than its perimeter, depending on its dimensions?" These curiosities can generate discussions and encourage students to explore the topic further. (1 - 2 minutes)

Development (20 - 25 minutes)

1. Activity 1: Building Rectangles and Parallelograms (10 - 12 minutes)

   • Description:
     • The teacher provides students with toothpicks and modeling clay.
     • Students must form rectangles and parallelograms using the toothpicks as sides and the clay as vertices.
   • Step by step:
     1. The teacher divides the class into groups of 3 to 4 students.
     2. Each group receives an equal amount of toothpicks and modeling clay.
     3. The teacher explains that the clay will be used to form the vertices of the rectangles and parallelograms, and the toothpicks will be the sides.
     4. Students must work together to form as many rectangles and parallelograms as possible.
     5. While students build the figures, the teacher circulates around the room, asking guiding questions and providing feedback.
     6. After all groups finish, the teacher asks them to compare the constructed figures and discuss the similarities and differences between rectangles and parallelograms.
     7. The teacher then introduces the area formula for rectangles and parallelograms and explains that the area is calculated by multiplying the base by the height.
     8. The teacher demonstrates how to measure the base and height of each constructed figure and how to use these measurements to calculate the area.

2. Activity 2: Area Challenge (10 - 13 minutes)

   • Description:
     • The teacher presents students with a series of problems involving the calculation of the area of rectangles and parallelograms.
     • Students must solve the problems in their groups, using the area formula and the figures they built in the previous activity.
   • Step by step:
     1. The teacher presents the problems one at a time, allowing a few minutes for the groups to discuss and come up with a solution.
     2. The problems should vary in difficulty and complexity, allowing students to apply the area formula in different contexts.
     3. While students work on the problems, the teacher circulates around the room, providing support when needed and observing the resolution process.
     4. After all problems are solved, the teacher asks some groups to share their solutions and explanations with the class.
     5. The teacher concludes the activity by highlighting the main points and clarifying any doubts that may have arisen.

Return (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes):

   • Description:
     • The teacher facilitates a group discussion where each team has the opportunity to share their solutions and conclusions.
     • The teacher should encourage students to explain how they arrived at the answer to each problem, highlighting the calculations made and the logic applied.
   • Step by step:
     1. The teacher asks each group to select a representative to share their solutions with the class.
     2. The representative of each group should summarize the problems they solved, highlighting the strategies used and the results obtained.
     3. While the representatives speak, the other students should pay attention and ask questions if necessary.
     4. The teacher should facilitate the discussion, clarifying doubts, asking probing questions, and connecting the groups' solutions with the presented theory.
     5. After all presentations, the teacher should summarize the main points, reinforcing the importance of area calculation and the difference between rectangles and parallelograms.

2. Connection with Theory (3 - 5 minutes):

   • Description:
     • After the discussion, the teacher should provide a brief recap of the theory, connecting it with the practical activities carried out by the students.
     • The teacher should reinforce the concept of area, explain again the formula for calculating the area of rectangles and parallelograms, and highlight the differences between these two figures.
   • Step by step:
     1. The teacher initiates the connection with the theory by asking students what the main concepts learned during the activities were.
     2. The teacher then explains how the practical activities helped illustrate and consolidate these concepts.
     3. The teacher should make specific reference to the groups' solutions, highlighting examples of how the area formula was correctly applied.
     4. The teacher may also mention some common errors observed during the activities and explain how to avoid them.
     5. The teacher concludes the connection with the theory by reinforcing the importance of area calculation and the ability to distinguish between rectangles and parallelograms.

3. Learning Reflection (2 - 3 minutes):

   • Description:
     • Finally, the teacher proposes that students reflect on what they learned during the lesson.
     • The teacher asks questions to guide students' reflection and encourages them to think about how what they learned can be applied in other situations or contexts.
   • Step by step:
     1. The teacher initiates the reflection by asking students what the most important concept learned during the lesson was.
     2. Next, the teacher asks students to think for a moment and internally answer the question: "How can I apply what I learned today in my daily life?"
     3. The teacher then asks some students to share their answers, which can range from the direct application of area calculation in practical situations to the importance of problems solving and teamwork.
     4. The teacher concludes the reflection by reinforcing the relevance of the learning to students' lives and encouraging them to continue exploring and applying the concepts learned.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes)

   • The teacher should recap the main points covered during the lesson: the concept of area, the formula for calculating the area of rectangles and parallelograms, the difference between these two figures, and how to apply the area formula in real situations.
   • It is important for the teacher to make connections between theory and the practical activities carried out by students, reinforcing the understanding of concepts and the application of acquired skills.

2. Connection of Theory, Practice, and Applications (1 - 2 minutes)

   • The teacher should explain how the lesson connected theory (mathematical concepts), practice (activities of building figures and problem-solving), and applications (real situations involving area calculation).
   • It should be emphasized that theory provides the basis for solving practical problems and understanding real-world applications, and that practical activities help consolidate theory and develop critical thinking and problem-solving skills.

3. Supplementary Materials (1 - 2 minutes)

   • The teacher should suggest supplementary study materials for students who wish to deepen their knowledge on the lesson topic. These may include: textbooks, educational websites, explanatory videos, math games, among others.
   • It is important that the suggested materials are suitable for the students' comprehension level and can be easily accessed and used at home.

4. Importance of the Topic in Daily Life (1 minute)

   • Finally, the teacher should reinforce the importance of calculating the area of rectangles and parallelograms in daily life. They can mention practical examples again, such as calculating the area of a plot of land, determining the amount of paint needed to paint a wall, among others.
   • The teacher can also remind students that the critical thinking and problem-solving skills developed during the lesson are useful and applicable in many other life situations.