Objectives (5 - 10 minutes)

1. Understand the definition and properties of a rhombus:

   • Identify the definition of a rhombus as a quadrilateral with congruent sides and two consecutive congruent angles.
   • Recognize the properties of a rhombus, such as the diagonals, which are perpendicular and bisect the angles of the rhombus.

2. Identify and describe the calculations involved in the properties of a rhombus:

   • Understand and apply the formula for the area of a rhombus: (larger diagonal x smaller diagonal) / 2.
   • Understand and use the formula for the perimeter of a rhombus: 4 x side length.

3. Solve practical and contextual problems involving rhombuses:

   • Apply the acquired knowledge to solve real-world problems related to rhombuses, such as determining the areas of diamond-shaped plots.

Secondary Objectives:

• Develop critical thinking and problem-solving skills: Through problem-solving involving rhombuses, students will be encouraged to think critically and apply the concepts learned in a practical way.
• Promote collaboration and discussion in the classroom: Students will be encouraged to work in groups, discussing and sharing their strategies for problem-solving, promoting collaboration and effective communication.

Introduction (10 - 15 minutes)

1. Reviewing necessary content: The teacher starts the lesson by reviewing the concepts of quadrilaterals and their properties. It is important to review that a quadrilateral is a flat figure with four sides and four angles, and that there are different types of quadrilaterals, each with its own characteristics and properties. This review should include the concepts of congruence of sides and angles. (2 - 3 minutes)

2. Problem situations: The teacher presents two problem situations to arouse students' interest and contextualize learning:

   • Situation 1: 'Imagine you are a civil engineer and need to calculate the area of a diamond-shaped plot. How would you do that?'
   • Situation 2: 'Suppose you work in a jewelry factory and need to create a pendant in the shape of a rhombus. How would you determine the length of the pendant's sides?' (3 - 5 minutes)

3. Contextualization: The teacher explains the importance of the rhombus in the real world, presenting examples of its application in various areas, such as engineering (in the design of bridges and structures), architecture (in facade and floor projects), art (in paintings and sculptures), and jewelry (in projects of rings, pendants, and earrings). (2 - 3 minutes)

4. Introducing the topic: The teacher then introduces the topic of the lesson, revealing that the focus will be on the rhombus, a special type of quadrilateral, its characteristics, and properties. To arouse students' curiosity, the teacher can share some curiosities about rhombuses, such as the fact that they have been known since antiquity and were widely used in Greek architecture. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Activity 'Building Rhombuses' (10 - 15 minutes)

   • Necessary materials: Popsicle sticks, glue, ruler, marker, scissors.
   • Class division: Divide the class into groups of five students.
   • Activity description: Each group will receive a kit of materials to build a rhombus. They must follow the teacher's instructions to assemble the rhombus, ensuring that all sides are congruent and that two consecutive angles are congruent. After construction, students must measure the sides and angles of the rhombus and record the values.

2. Activity 'The World of Rhombuses' (10 - 15 minutes)

   • Necessary materials: Sheets of paper, pencils, ruler, calculator.
   • Activity description: Each group will receive a sheet of paper and the task of drawing a rhombus of the size they desire. They must then measure the diagonals of the rhombus and calculate the area and perimeter. After the calculations, students should discuss the relationships between the values obtained and the characteristics of the rhombus, such as the relationship between the diagonals and the angles. Students should also discuss how they could change the size of the rhombus to obtain different areas and perimeters.

3. Group Discussion (5 - 10 minutes)

   • Activity description: After completing the activities, each group will present their results to the class. They must explain how they built the rhombus, what measurements they obtained, and how they made the calculations. The teacher should facilitate the discussion by asking questions to ensure that students understood the properties of the rhombus and how they relate to the measurements obtained. The teacher should also use this moment to correct any misconceptions and reinforce important concepts.

These activities allow students to explore the concept of the rhombus in a practical and contextualized way, developing their critical thinking and problem-solving skills. In addition, group discussion promotes collaboration and effective communication, important skills for students' academic and professional success.

Return (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes)

   • Description: The teacher should promote a group discussion with all students, where each group shares their solutions for the activities 'Building Rhombuses' and 'The World of Rhombuses'. Students will have the opportunity to explain their methodologies, difficulties encountered, and the conclusions they reached. The teacher should encourage questions and comments from other students, promoting a collaborative environment and mutual learning.

2. Connection with Theory (3 - 5 minutes)

   • Description: After the group discussion, the teacher should summarize the main ideas discussed, connecting them with the theory presented at the beginning of the lesson. The teacher can reinforce how the constructions and measurements made by students relate to the formal properties of rhombuses, and how the calculations performed corroborate these properties.

3. Individual Reflection (2 - 3 minutes)

   • Description: The teacher should propose that students reflect individually on what they learned in the lesson. To do this, the teacher can ask the following questions:
     1. What was the most important concept you learned today?
     2. What questions have not been answered yet?
   • The teacher should give a minute for students to think about their answers. Then, some students will be invited to share their reflections with the class. This activity promotes the consolidation of learning and the identification of possible gaps in students' understanding.

4. Feedback and Closure (1 - 2 minutes)

   • Description: To end the lesson, the teacher can provide general feedback on the class's performance, highlighting strengths and areas that need more attention. The teacher can also provide guidance on how students can continue to practice and deepen the knowledge acquired. Finally, the teacher should thank the students for their participation and reinforce the importance of the rhombus in the mathematical context and in various everyday applications.

This Return moment is essential to consolidate students' learning, allowing them to reflect on what they have learned and identify any unanswered questions or issues. In addition, group discussion promotes the exchange of ideas and collaborative learning, fundamental skills for students' academic and personal development.

Conclusion (5 - 10 minutes)

1. Summary of Contents (2 - 3 minutes)

   • The teacher should give a brief summary of the main points covered in the lesson, reinforcing the concepts of the rhombus, its properties, and the formulas for calculating its area and perimeter.
   • It is important for the teacher to emphasize the definition of a rhombus as a quadrilateral with congruent sides and two consecutive congruent angles, and that the diagonals of a rhombus are perpendicular and bisect its angles.
   • The teacher should recap the formula for the area of a rhombus, which is (larger diagonal x smaller diagonal) / 2, and the formula for the perimeter of a rhombus, which is 4 x side length.

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

   • The teacher should reiterate how the practical activities carried out during the lesson helped to illustrate and solidify the theoretical concepts presented.
   • It should be highlighted how the construction and measurement of rhombuses allowed students to visualize and experience the properties and formulas of the rhombus.
   • The teacher can refer to the group discussions, explaining how they helped deepen students' understanding of the concepts and promote collaboration and the exchange of ideas.

3. Additional Materials (1 - 2 minutes)

   • The teacher should suggest additional study materials so that students can review and deepen the content learned in the lesson. This may include textbooks, educational websites, explanatory videos, and practical exercises.
   • For example, the teacher may suggest that students watch a video showing different ways to build a rhombus, or that they solve some math problems involving rhombuses.

4. Relevance of the Rhombus in Everyday Life (1 - 2 minutes)

   • Finally, the teacher should reinforce the importance of the rhombus in everyday life, highlighting its applications in various areas such as engineering, architecture, art, and jewelry.
   • For example, the teacher may mention how knowledge about rhombuses can be useful for a civil engineer in the construction and design of structures, or for a jewelry designer in creating new projects.
   • This connection between mathematics and the real world helps motivate students and demonstrate the relevance of what they are learning.

This Conclusion stage is essential to consolidate students' learning, reinforcing the most important concepts, making connections with practice and everyday life, and suggesting materials for additional study. In addition, the Conclusion also serves to motivate students and show the relevance of mathematics in their lives.