Objectives (5 - 7 minutes)

1. Understand the concept of Rectangle: Students should be able to define what a rectangle is and identify its main characteristics (congruent opposite sides and right internal angles). They should be able to differentiate a rectangle from other types of quadrilaterals.

2. Recognize the properties of Rectangle: Students should be able to list and explain the properties of a rectangle, including the property that states the sum of the internal angles of a rectangle is always 360 degrees. They should also be able to apply these properties to solve problems involving rectangles.

3. Identify and Draw Rectangles: Students should be able to identify rectangles in different contexts, such as in drawings, blueprints, everyday objects, etc. Additionally, they should be able to draw rectangles based on their properties and characteristics.

Secondary Objectives:

• Develop logical thinking and spatial visualization skills: By working with the concept of rectangles, students will have the opportunity to develop their logical thinking, problem-solving, and spatial visualization skills.

• Apply acquired knowledge in everyday situations: During the lesson, students will be encouraged to think of examples of rectangles in their everyday environment, helping them see the practical relevance of what they are learning.

Introduction (10 - 12 minutes)

1. Review of Previous Concepts: The teacher starts the lesson by briefly reviewing the concepts of quadrilaterals, specifically parallelograms, and their properties. They can remind students about what quadrilaterals are, how to identify a quadrilateral, and the types of quadrilaterals based on their properties. This will set the stage for the introduction of the specific topic of the lesson - rectangles. (3 - 5 minutes)

2. Problem-Solving Situations: The teacher can propose two situations to stimulate students' curiosity and thinking:

   • The first situation could be: "Imagine you are building a wall in your backyard and it needs to be straight with 90-degree angles. How can you make sure the wall you built is a rectangle?"
   • The second situation could be: "Think about a tablet or smartphone. What shape are most of them? Why are they like that?"

   These situations aim to arouse students' curiosity, leading them to question and think about the importance of rectangles in our daily lives. (2 - 3 minutes)

3. Contextualization: The teacher should contextualize the importance of rectangles in the real world, mentioning examples such as:

   • In architecture and construction, rectangles are used to ensure right angles and structural shapes.
   • In graphic design and visual arts, rectangles are often used as a base for compositions and layouts.
   • In technology, rectangles are the basis for many electronic devices, such as computer screens, TVs, and smartphones. (2 - 3 minutes)

4. Introduction to the Topic: The teacher then introduces the topic of rectangles in an engaging way, mentioning curiosities such as:

   • "Did you know that the term 'rectangle' comes from the Latin 'rectangulum', which means 'right angle'? This is because the most striking feature of a rectangle is its four internal angles equal to 90 degrees."
   • "Have you heard of the 'Pythagorean Theorem', right? It is very useful when working with rectangles, as it allows us to calculate the length of one side when we know the other two."

   These curiosities are great ways to draw students' attention to the topic and start a lively discussion. (3 - 4 minutes)

Development (20 - 25 minutes)

1. Theory Presentation (10 - 12 minutes):

   1.1. Rectangle Definition: The teacher begins the theory presentation by reinforcing the definition of a rectangle as a quadrilateral that has four internal angles of 90 degrees. They should highlight that a rectangle is a special type of parallelogram, where opposite sides are congruent. (2 - 3 minutes)

   1.2. Rectangle Properties: The teacher then introduces the properties of rectangles: the sum of the internal angles of a rectangle is always 360 degrees; opposite sides are congruent; the diagonals are congruent and intersect at their midpoints. The teacher should explain each property and provide visual examples to aid in understanding. (3 - 4 minutes)

   1.3. Related Theorems: The teacher can mention some theorems related to rectangles, such as the Pythagorean Theorem, which can be used to calculate the length of one side of a rectangle if the other two sides are known. Another theorem is the Thales' Theorem, which establishes a proportional relationship between the diagonals of a rectangle and its sides. (2 - 3 minutes)

   1.4. Practical Applications: To reinforce the relevance of rectangles, the teacher should present some practical applications, such as the use of rectangles in architecture and engineering to build structures with right angles, or in electronics manufacturing, where many devices, like tablets and smartphones, have the shape of a rectangle. (2 - 3 minutes)

2. Example Resolution (10 - 12 minutes):

   2.1. Example 1: The teacher presents a problem for the students to solve together. For example, "If the diagonal of a rectangle measures 10 cm and one of the sides measures 6 cm, what is the length of the other side?" The teacher should guide the students to identify the given information, the property or theorem that can be applied, and the strategy to solve the problem. Then, the students solve the problem, with the teacher guiding and supporting as needed. (4 - 5 minutes)

   2.2. Example 2: The teacher presents another problem for the students to solve in small groups. For example, "Draw a rectangle where one side measures 5 cm and the height is 3 cm." The teacher should guide the students to draw the rectangle, reminding them of the rectangle's properties, such as right angles and congruent opposite sides. (4 - 5 minutes)

3. Practical Activity (5 - 8 minutes):

   3.1. Drawing Activity: The teacher can propose a drawing activity where students must draw rectangles on grid paper based on different given measurements. For example, "Draw a rectangle where the length is 4 units and the width is 3 units." This activity will help students visualize and better understand the properties of rectangles. (3 - 4 minutes)

   3.2. Identification Activity: The teacher can bring images of everyday objects, house blueprints, maps, etc., and ask students to identify the rectangles present in them. This activity will help students see the presence and importance of rectangles in our daily lives. (2 - 3 minutes)

The teacher should circulate around the room throughout the activity, assisting students, clarifying doubts, and providing guidance as needed. The goal is to ensure all students are engaged and understanding the content. Additionally, the teacher should encourage discussion among students so they can learn from each other and develop their critical thinking skills.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): The teacher should facilitate a group discussion where students share their solutions and conclusions from the activities. The teacher can ask open-ended questions to stimulate student participation, such as:

   1.1. "What strategies did each group use to draw the rectangle with the given measurements?" 1.2. "How did you apply the properties of the rectangle to solve the drawing activity problem?" 1.3. "Which rectangles were you able to identify in the identification activity? Why do you think these objects were designed in the shape of rectangles?"

   The teacher should encourage students to explain their reasoning and listen attentively to each other's contributions. This not only reinforces students' learning but also helps develop their communication and cooperation skills.

2. Connection to Theory (2 - 3 minutes): The teacher should then make the connection between the practical activities carried out and the theory presented. They should emphasize how the properties of rectangles were applied in the problem-solving and drawing activities, and how identifying rectangles in everyday situations demonstrates the relevance and applicability of the theoretical content. The teacher can ask questions like:

   2.1. "How did the drawing activity help reinforce the idea that in a rectangle the internal angles are always right angles and the opposite sides are congruent?" 2.2. "How did the identification activity of rectangles in everyday life demonstrate the relevance of what we learned about rectangles?"

   The goal is to make students feel confident that they understood the concept of rectangles and their properties, and that they are able to apply this knowledge in different contexts.

3. Final Reflection (3 - 4 minutes): Finally, the teacher should propose that students reflect individually for a minute on the following questions:

   3.1. "What was the most important concept you learned today about rectangles?" 3.2. "What questions have not been answered yet?"

   After the reflection time, the teacher can ask some students to share their answers with the class. This not only helps the teacher assess the effectiveness of the lesson but also allows students to consolidate their learning and identify any gaps in their understanding that can be addressed in future lessons.

The Return is a crucial part of the lesson plan as it allows the teacher to assess students' progress, reinforce what was learned, clarify any misunderstandings, and motivate students to continue learning.

Conclusion (5 - 7 minutes)

1. Summary and Recapitulation (2 - 3 minutes): The teacher should give a brief summary of the key points of the lesson. They can start by recalling the definition of a rectangle, its main characteristics, and the properties that distinguish it from other quadrilaterals. Then, they should recapitulate the theorems and concepts related to rectangles, such as the Pythagorean Theorem and Thales' Theorem. The teacher should also highlight the practical applications of rectangles, emphasizing their presence in students' daily lives, whether in architecture, engineering, design, or even in electronic devices.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes): The teacher should emphasize how the lesson connected theory, practice, and applications. They can mention the problem-solving and drawing activities that allowed students to apply the properties of rectangles in a practical way. Additionally, the teacher should reinforce the relevance of the practical applications of rectangles discussed during the lesson for the understanding and appreciation of the theoretical content.

3. Extra Materials (1 - 2 minutes): The teacher should suggest some extra materials for students who wish to deepen their understanding of rectangles. These materials may include math books, educational websites, explanatory videos, online games, and math apps. For example, the teacher can recommend the use of an app that allows students to explore the properties of rectangles through virtual drawings and manipulations.

4. Relevance of the Topic (1 - 2 minutes): Finally, the teacher should emphasize the importance of the topic learned for students' daily lives. For example, they can mention that understanding rectangles can help students make measurements and calculations in their daily activities, better understand the world around them, and prepare for future studies in mathematics and other areas involving geometry and spatial thinking.

The conclusion of the lesson is an opportunity for the teacher to reinforce the concepts learned, connect theory to practice and applications, and motivate students to continue learning about the topic. Additionally, by suggesting extra materials and highlighting the relevance of the topic to students' daily lives, the teacher is encouraging autonomous learning and the application of acquired knowledge in different contexts.