Objectives (5 minutes)

1. Understand the concept of a rhombus: The main objective is for students to understand what a rhombus is, its characteristics, and properties. This includes recognizing that a rhombus is a quadrilateral with congruent sides and perpendicular diagonals and bisectors.

2. Identify the elements of a rhombus: Students should be able to identify and describe the main elements of a rhombus, such as sides, angles, diagonals, and bisectors.

3. Solve problems involving rhombuses: Through the application of acquired knowledge, students should be able to solve practical problems involving rhombuses. This may include determining areas, perimeters, and other specific properties.

Secondary Objectives:

• Develop logical and mathematical reasoning skills: Through the exploration of the rhombus concept, students should be able to enhance their logical and mathematical reasoning skills.

• Promote active learning: The lesson plan is designed to encourage active student participation, allowing them to explore and discover the concept of a rhombus through practical activities.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher should start the lesson by reviewing basic concepts of quadrilaterals, such as parallelograms, trapezoids, rectangles, and squares. This review can be done interactively, asking students to identify these types of quadrilaterals in figures projected on the board or on their desks. (5 minutes)

2. Presentation of problem situations: To introduce the topic of rhombuses, the teacher can propose two problem situations:

   • Situation 1: 'Imagine you are building a mosaic on the ground of a square and need to create a design with stones in the shape of a rhombus. How can you make sure that all the stones used are rhombuses?'

   • Situation 2: 'Suppose you have a piece of paper in the shape of a rhombus and want to cut an equilateral triangle from it. How can you determine the size of the triangle that can be cut?' (5 minutes)

3. Contextualization of the importance of the rhombus: The teacher should then explain how rhombuses are often found in everyday life, from mosaic designs to diamond shapes. Additionally, it should be mentioned that the study of rhombuses is important for geometry and for various practical applications, such as in architecture and design. (3 minutes)

4. Introduction of the topic with curiosities: To spark students' interest, the teacher can share some curiosities about rhombuses:

   • Curiosity 1: 'Did you know that the rhombus is the only quadrilateral that has all congruent diagonals?'

   • Curiosity 2: 'Did you know that the word 'rhombus' comes from the Greek 'losangos', which means 'four angles'? This gives us a clue about one of its main characteristics.' (2 minutes)

Development (20 - 25 minutes)

1. Rhombus Construction Activity (10 - 15 minutes)

   • Necessary materials: Grid paper, ruler, pencil, and different colors for students to distinguish the sides of the rhombus.

   • Group division: Students will be divided into groups of up to 5 members.

   • Instructions: The teacher should instruct each group to construct two different rhombuses on their grid paper. One of the rhombuses should have sides of length 5 units and the other of length 7 units.

   • Task: Students should measure the internal angles and diagonals of their rhombuses and record the measurements. They should also color the sides of the rhombus in a way that opposite sides have the same color.

   • Discussion: After completing the activity, the teacher should lead a classroom discussion about the students' findings. The groups should share the measurements they found and the strategies they used to construct the rhombuses. The teacher should reinforce the concept that all sides of a rhombus are congruent and that the diagonals are perpendicular and bisectors.

2. Rhombus Area Calculation Activity (10 - 15 minutes)

   • Necessary materials: Same grid paper, ruler, pencil, and different colors.

   • Instructions: The teacher should propose that the groups calculate the area of one of the rhombuses they constructed in the previous activity. They should use the rhombus area formula (Area = base x height / 2) with the longer diagonal as the base and the shorter diagonal as the height.

   • Task: Students should perform the calculations and record the area found. They should also draw a rhombus on another grid paper with the calculated area and verify if it is possible to construct a rhombus with that area.

   • Discussion: After completing the activity, the teacher should lead another classroom discussion, this time focusing on the areas of rhombuses. Students should share the areas they calculated and the strategies they used. The teacher should reinforce that the area of a rhombus is always half the product of its diagonals.

3. Problem-Solving Activity with Rhombuses (5 - 10 minutes)

   • Necessary materials: Grid paper, ruler, pencil, and different colors.

   • Instructions: The teacher should propose a series of problems involving rhombuses for the groups to solve. The problems may include determining the perimeter, finding an unknown diagonal, and calculating a diagonal from the area.

   • Task: Groups should work together to solve the proposed problems. They should use the properties of rhombuses they learned to find the solutions.

   • Discussion: The teacher should lead a classroom discussion to check the solutions found by the groups and clarify any doubts that may have arisen. This is an opportunity to reinforce the concept of a rhombus and its properties.

These practical and playful activities allow students to explore and understand the concept of a rhombus in an active and engaging way. Additionally, they promote teamwork, logical reasoning, and critical thinking.

Return (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes)

   • The teacher should gather all students for a classroom discussion. Each group will have a maximum of 3 minutes to share their solutions or conclusions from the activities carried out. During the presentations, the teacher should encourage other groups to ask questions and share their own ideas.

   • The teacher should take this opportunity to highlight the effective strategies used by different groups and explain how they relate to the concepts of a rhombus. This will help consolidate students' knowledge and improve their problem-solving skills.

2. Connection to Theory (3 - 5 minutes)

   • After the presentations, the teacher should give a quick review of the theoretical concepts covered in the lesson. They should emphasize how these concepts were applied in the practical activities and how they helped students solve the proposed problems.

   • The teacher can use examples from the group presentations to illustrate how theory is applied in practice. This will help students understand the relevance and usefulness of rhombus concepts.

3. Individual Reflection (2 - 3 minutes)

   • To conclude the lesson, the teacher should propose that students reflect individually on what they have learned. They should ask questions like:

     1. 'What was the most important concept you learned today?'
     2. 'What questions do you still have about rhombuses?'

   • Students should have a minute to think and write down their answers. Then, they will be invited to share their reflections with the class, if they wish. The teacher should encourage all students to participate, ensuring that each opinion is valued.

4. Teacher Feedback (1 minute)

   • Finally, the teacher should provide overall feedback on the class participation, highlighting the positive aspects and areas that still need improvement. They should also reinforce the importance of the rhombus concept for mathematics and everyday life, encouraging students to continue exploring and practicing what they have learned.

Conclusion (5 - 7 minutes)

1. Recap of Main Contents (2 - 3 minutes):

   • The teacher should summarize the main points covered during the lesson, reiterating the concept of a rhombus as a quadrilateral with congruent sides and perpendicular diagonals and bisectors.

   • They should also recall the properties of the rhombus, such as the congruence of diagonals and the perpendicularity between them, the bisection of internal angles, and the existence of congruent internal angles.

   • Finally, they should reinforce the rhombus area formula as half the product of its diagonals and the way to calculate the rhombus perimeter.

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

   • The teacher should highlight how the lesson was structured to promote the connection between the theory, practice, and applications of the rhombus concept.

   • They should emphasize how the practical activities allowed students to explore and discover the properties of the rhombus and how this applies to everyday situations, such as mosaic construction or paper cutting.

3. Suggestions for Additional Materials (1 minute):

   • The teacher should suggest additional study materials for students who wish to deepen their knowledge of rhombuses. This may include readings, explanatory videos, online math games, and practical exercises.

   • For example, the teacher may recommend a YouTube video that explains the properties of the rhombus visually and interactively, or an online game that challenges students to solve problems involving rhombuses.

4. Importance of the Rhombus in Everyday Life (1 minute):

   • Finally, the teacher should emphasize the importance of the rhombus in everyday life and in various areas of knowledge, such as architecture, design, jewelry, engineering, and physics.

   • They should stress that by understanding and being able to work with rhombuses, students are acquiring essential mathematical skills, such as the ability to visualize and manipulate shapes and the ability to solve problems in a logical and systematic manner.