Objectives (5 - 7 minutes)

1. Understand the formula for the area of a trapezoid: The main objective is for students to understand the formula and how it is derived. They should be able to explain the relationship between the area of the trapezoid and the measurements of its larger base, smaller base, and height.

2. Apply the formula for the area of a trapezoid in problem-solving situations: Once the formula is understood, students should be able to use it to solve practical problems. They should be able to identify relevant information in a problem and apply the formula correctly to find the area of the trapezoid.

3. Differentiate the trapezoid from other polygons: In addition to calculating the area of the trapezoid, students should be able to distinguish a trapezoid from other polygons. They should understand that a trapezoid has only one pair of parallel sides, while the other sides are not parallel.

Secondary Objectives:

• Stimulate critical thinking and problem-solving: Through problem-solving involving the area of the trapezoid, students should develop their critical thinking skills and the ability to solve problems effectively.

• Promote teamwork: Practical activities should be carried out in groups, encouraging collaboration among students and the development of teamwork skills.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher begins the lesson by reviewing the concepts of the area of plane figures already studied, such as the area of the rectangle and the triangle. These concepts are fundamental for understanding the calculation of the area of the trapezoid. (3 - 5 minutes)

2. Introductory problem-solving situations: To spark students' interest, the teacher can present two problem-solving situations:

   • Problem 1: 'Imagine you have a soccer field that is a trapezoid, and you need to calculate its area to plant grass. How would you do that?'
   • Problem 2: 'Suppose you have a piece of paper that is a trapezoid, and you need to calculate how many square centimeters of paper you have. How would you do that?' (3 - 5 minutes)

3. Contextualization: The teacher explains that the area of the trapezoid is an important tool in various practical situations, such as in construction, architecture, engineering, and even in everyday activities, such as preparing a recipe and needing to calculate the area of a cake pan. (2 - 3 minutes)

4. Introduction to the topic: The teacher formally introduces the topic of the lesson, explaining that the trapezoid is a polygon with particular characteristics and that, to calculate its area, a specific formula must be used. The teacher also mentions that although the formula may seem complex initially, it is actually quite simple and logical. (2 - 3 minutes)

5. Curiosity: To further pique students' interest, the teacher can share some curiosities about the trapezoid, such as the fact that the term 'trapezoid' originates from the Greek word 'trapezion', which means 'small table' due to the resemblance of the trapezoid's shape to a table. Another curiosity is that the trapezoid is one of the few polygons whose area can be calculated relatively simply, without the need to subdivide the figure into triangles. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Activity 'Building a Trapezoid' (10 - 12 minutes):

   • Description: In this activity, students, divided into groups of up to five people, will receive materials such as popsicle sticks, strings, and scissors. They should, following the teacher's instructions, build a trapezoid using these materials.

   • Objective: The objective of this activity is to allow students to visualize and manipulate a trapezoid, based on a construction made by themselves, as well as to encourage collaboration and teamwork.

   • Step by step:

     1. The teacher distributes the materials to each group.
     2. Next, the teacher shows how to draw a trapezoid on a piece of paper, explaining the characteristics and properties of this figure.
     3. The students then try to reproduce the trapezoid on their table using the available materials.
     4. Once all groups have built their trapezoids, the teacher circulates around the room, checking and correcting if necessary.
     5. Finally, the teacher gathers the class and discusses the similarities and differences between the constructed trapezoids, reinforcing the characteristics of this figure.

2. Activity 'Trapezoid in real life' (10 - 12 minutes):

   • Description: In this activity, students, still in their groups, will be challenged to find examples of trapezoids in everyday objects. They should record their findings and share them with the class.

   • Objective: The objective of this activity is to make students realize how the trapezoid is present in our daily lives, making the concept more concrete and applicable.

   • Step by step:

     1. The teacher explains the activity and provides paper and pencils to the groups to record their findings.
     2. The students start looking for trapezoids in nearby objects, such as packaging, frames, windows, etc.
     3. As they find examples, the students draw the object and highlight the trapezoid. They also note the function or use of the object.
     4. After a few minutes, the teacher asks the groups to share their findings, explaining why they identified the object as a trapezoid.
     5. The teacher concludes the activity by reinforcing the presence of the trapezoid in our daily lives and the importance of understanding and applying the formula for the area of this polygon.

3. Activity 'Solving problems with the trapezoid' (5 - 8 minutes):

   • Description: In this final activity, students, still in groups, will receive a series of problems involving the calculation of the area of the trapezoid. They should work together to solve the problems, applying the formula and discussing their solutions.

   • Objective: The objective of this activity is to allow students to apply what they have learned about the area of the trapezoid in real and complex situations, developing their problem-solving skills.

   • Step by step:

     1. The teacher distributes the problems to each group.
     2. The students, in their groups, discuss the problems, identifying relevant information and planning the strategy for the solution.
     3. Once they have found a solution, the students record it and present it to the class, explaining step by step how they arrived at that solution.
     4. The teacher then discusses the solution with the class, clarifying any doubts and reinforcing the concepts and the formula for the area of the trapezoid.

The teacher should circulate around the room, assisting the groups, clarifying doubts, and monitoring the progress of the activities. At the end of each activity, the teacher should promote a class discussion to consolidate learning and clarify any doubts that may have arisen.

Return (8 - 10 minutes)

1. Group discussion (3 - 4 minutes):

   • Description: The teacher gathers all students and promotes a group discussion about the solutions found by each group in the activities 'Trapezoid in real life' and 'Solving problems with the trapezoid'.
   • Objective: The objective of this discussion is to allow students to share their solutions, ideas, and challenges, promoting collaborative learning and the development of communication skills.
   • Step by step:
     1. The teacher requests each group to briefly share their findings and solutions.
     2. Students have a limited time (for example, 1 minute) to present their ideas.
     3. After all presentations, the teacher facilitates a discussion, highlighting the similarities and differences between the solutions presented, and encouraging students to ask questions and make comments.

2. Connection with theory (2 - 3 minutes):

   • Description: Based on the solutions presented and the group discussion, the teacher bridges the gap between the practice of the activities and the theory presented in the Introduction of the lesson.
   • Objective: The objective is to reinforce theoretical concepts, demonstrating how they apply in practical and real situations.
   • Step by step:
     1. The teacher highlights the main ideas and strategies presented by the groups and relates them to the formula for the area of the trapezoid.
     2. The teacher explains how the theory was applied in practice to solve the problems in the activities.
     3. The teacher can also take the opportunity to clarify any doubts that may have arisen during the activities.

3. Individual reflection (3 - 4 minutes):

   • Description: The teacher proposes that students reflect individually on what they learned during the lesson, and identify possible doubts or difficulties.
   • Objective: The objective is for students to internalize the learned content, evaluate their own understanding, and identify any gaps in their knowledge.
   • Step by step:
     1. The teacher proposes some questions to guide students' reflection, such as: 'What was the most important concept you learned today?' and 'What questions have not been answered yet?'.
     2. Students have a minute to reflect on these questions.
     3. Then, the teacher asks some students to share their answers, promoting a brief discussion.
     4. The teacher records the main doubts or difficulties identified by the students, to guide the preparation of the next lessons.

The teacher should end the lesson by reinforcing the main points learned, praising the effort and participation of the students, and encouraging them to continue studying and practicing the calculation of the area of the trapezoid.

Conclusion (5 - 7 minutes)

1. Content summary (2 - 3 minutes):

   • Description: The teacher summarizes the main points covered during the lesson, reinforcing the definition of the trapezoid, the formula for the area and how it is derived, and the steps to calculate the area of the trapezoid.
   • Objective: The objective is to consolidate learning, reviewing fundamental concepts and clarifying any final doubts students may have.
   • Step by step:
     1. The teacher briefly reviews the definition of the trapezoid and its characteristics.
     2. Next, the teacher reaffirms the formula for the area of the trapezoid and how it is derived, highlighting the importance of the bases and the height.
     3. Finally, the teacher recalls the steps to calculate the area of the trapezoid, emphasizing the need to identify the bases and the height correctly.

2. Connection between theory, practice, and applications (1 - 2 minutes):

   • Description: The teacher explains how the lesson connected the theory, practice, and applications of calculating the area of the trapezoid.
   • Objective: The objective is to show students the relevance of what they have learned, demonstrating that mathematics is not just an abstract discipline, but a useful and applicable tool.
   • Step by step:
     1. The teacher highlights how the practical activities allowed students to visualize and manipulate a trapezoid, making the concept more concrete.
     2. The teacher reinforces how solving problems with the trapezoid helped apply theory in a practical way.
     3. The teacher mentions the various real-life applications of calculating the area of the trapezoid, showing students that what they have learned is relevant outside the classroom.

3. Extra materials (1 - 2 minutes):

   • Description: The teacher suggests extra materials for students who wish to deepen their knowledge of calculating the area of the trapezoid.
   • Objective: The objective is to encourage autonomous study, providing students with additional resources to explore the subject more widely and deeply.
   • Step by step:
     1. The teacher recommends mathematics books that have sections dedicated to plane geometry and area calculation.
     2. The teacher suggests educational websites that offer videos, interactive tutorials, and online exercises on calculating the area of the trapezoid.
     3. The teacher can also recommend math apps that have games and activities related to area calculation.

4. Importance of the subject (1 minute):

   • Description: Finally, the teacher emphasizes the importance of calculating the area of the trapezoid, not only as a mathematical concept, but as a practical skill.
   • Objective: The objective is to motivate students to continue studying and practicing, showing that what they have learned is valuable and has real-world applications.
   • Step by step:
     1. The teacher mentions some of the practical applications of calculating the area of the trapezoid, such as in architecture, engineering, cooking, among others.
     2. The teacher encourages students to continue practicing, reminding them that mathematics, like any other skill, improves with practice and effort.