Lesson Plan | Traditional Methodology | Quadrilateral: Parallelogram

Objectives

Duration: 10 to 15 minutes

The purpose of this stage of the lesson plan is to introduce students to the concept of a parallelogram, allowing them to understand its basic characteristics and properties. In addition, this stage prepares students to calculate measures related to the sides and angles of a parallelogram and to solve practical problems that involve this geometric figure.

Main Objectives

1. Understand what a parallelogram is.

2. Calculate measures of sides and angles in a parallelogram.

3. Solve problems that involve parallelograms.

Introduction

Duration: 10 to 15 minutes

The purpose of this stage of the lesson plan is to introduce students to the concept of a parallelogram, allowing them to understand its basic characteristics and properties. In addition, this stage prepares students to calculate measures related to the sides and angles of a parallelogram and to solve practical problems that involve this geometric figure.

Context

To start the lesson on parallelograms, it is interesting to place students in the world of flat geometric shapes. Explain that quadrilaterals, which are figures with four sides, often appear in our daily lives. Among quadrilaterals, parallelograms stand out, having special properties that make them very useful in various applications. Using visual examples, such as a cell phone screen or the surface of a table, can help students easily visualize the relevance of this concept.

Curiosities

Did you know that many of the objects we use daily, such as books, computer screens, and even some building designs, are based on the shape of parallelograms? Engineers and architects use the properties of parallelograms to ensure that their constructions are stable and functional. Furthermore, in art, many mosaic and fabric patterns use this shape to create symmetrical and aesthetically pleasing designs.

Development

Duration: 45 to 50 minutes

The purpose of this stage of the lesson plan is to deepen students' understanding of parallelograms, covering their properties, measurement calculations, and problem-solving. This stage aims to consolidate the concepts presented and ensure that students are able to apply the knowledge acquired in practical situations.

Covered Topics

1. Definition of Parallelogram: Explain that a parallelogram is a quadrilateral in which the opposite sides are parallel. This characteristic implies that the opposite sides are of equal length and the opposite angles are equal. 2. Properties of Parallelograms: Discuss the main properties of parallelograms, such as opposite sides being congruent, opposite angles being congruent, the diagonals bisecting each other, and adjacent angles being supplementary (summing to 180 degrees). 3. Calculation of Sides and Angles: Show examples of how to calculate the sides and angles of a parallelogram using its properties. For example, if one angle is known, the opposite angle is equal, and the adjacent angles sum to 180 degrees. 4. Practical Examples: Provide practical examples involving parallelograms in realistic situations, such as in engineering and architecture problems. Use visual figures to illustrate the concepts. 5. Problem Solving: Guide the students in solving problems involving parallelograms, leading them step by step so they understand how to apply the discussed properties and formulas.

Classroom Questions

1. What is the measure of the angle opposite to a 70-degree angle in a parallelogram? Explain your answer. 2. If a parallelogram has one side of 8 cm and the opposite side is 5 cm, what are the lengths of the other two sides? Justify your answer. 3. In a parallelogram, the diagonals bisect each other. If one diagonal measures 16 cm and the other measures 12 cm, what is the length of each segment into which the diagonals divide?

Questions Discussion

Duration: 25 to 30 minutes

The purpose of this stage of the lesson plan is to verify students' understanding of the concepts taught, allowing for the correction of any doubts and the consolidation of knowledge. Discussing the resolved questions and engaging students in deeper reflections ensures that they are capable of applying the properties of parallelograms in different contexts and problems.

Discussion

• What is the measure of the angle opposite to a 70-degree angle in a parallelogram? Explain your answer.

• Since the opposite angles in a parallelogram are equal, if one of the angles is 70 degrees, the opposite angle will also be 70 degrees. Additionally, the adjacent angles sum to 180 degrees. Therefore, the angle adjacent to 70 degrees will be 110 degrees (180 - 70 = 110).

• If a parallelogram has one side of 8 cm and the opposite side is 5 cm, what are the lengths of the other two sides? Justify your answer.

• In a parallelogram, opposite sides are equal. Therefore, if one side measures 8 cm, the opposite side will also measure 8 cm. Similarly, if one side measures 5 cm, the opposite side will also measure 5 cm. Thus, the lengths of the other two sides are 8 cm and 5 cm.

• In a parallelogram, the diagonals bisect each other. If one diagonal measures 16 cm and the other measures 12 cm, what is the length of each segment into which the diagonals divide?

• The diagonals of a parallelogram bisect each other, meaning that each diagonal is divided in half by the point of intersection. Therefore, if one diagonal measures 16 cm, each segment will measure 8 cm (16 / 2 = 8). If the other diagonal measures 12 cm, each segment will measure 6 cm (12 / 2 = 6).

Student Engagement

1.  Discussion Questions: 2. How would you apply the concept of supplementary angles to solve problems involving parallelograms? 3. Why is it important to know that the diagonals of a parallelogram bisect each other? How can this be useful in practical problems? 4. In what practical situations can you identify the presence of parallelograms and apply these properties? 5. If a parallelogram has two adjacent angles of 80 degrees and 100 degrees, how would you determine the measures of the opposite angles? 6. If the diagonals of a parallelogram are equal, what special type of parallelogram is it? Explain. 7.  Reflections: 8. Reflect on how understanding the properties of parallelograms can help in other areas of mathematics, such as analytic geometry and algebra. 9. Think about how the concepts of parallelograms can be applied in design and architecture. What are the benefits of using these shapes in constructions?

Conclusion

Duration: 10 to 15 minutes

The purpose of this stage of the lesson plan is to consolidate the knowledge acquired by students, recapping the main points covered and reflecting on the practical importance of parallelograms. This stage allows students to make clear connections between theory and its applications, reinforcing the relevance of the content studied.

Summary

• Definition of parallelogram as a quadrilateral with opposite sides parallel.
• Properties of parallelograms: opposite sides are congruent, opposite angles are congruent, diagonals bisect each other, and adjacent angles are supplementary.
• Calculation of measures of sides and angles in a parallelogram.
• Resolution of practical problems involving parallelograms.

The lesson connected the theory of parallelograms with real practices and applications by using visual examples and practical problems related to engineering, architecture, and design. This allowed students to see how the properties of parallelograms are used in the real world to create stable and aesthetically pleasing structures.

Understanding parallelograms is essential for various fields of knowledge and daily life. From building construction to furniture design and creating artistic patterns, this geometric shape is fundamental to ensuring stability and symmetry. Moreover, knowledge about parallelograms can be applied in other areas of mathematics, such as analytic geometry and algebra.