Lesson Plan | Traditional Methodology | Polygons: Classification

Objectives

Duration: (10 - 15 minutes)

The aim of this stage is to lay the foundation for understanding the topic by outlining the main subjects that will be addressed during the lesson. This helps students know what to expect and focus on the specific skills they need to acquire, facilitating the assimilation of polygon concepts and their classification.

Main Objectives

1. Recognize what polygons are.

2. Classify polygons according to the number of sides.

3. Distinguish regular from irregular polygons.

Introduction

Duration: (10 - 15 minutes)

 Purpose: The aim of this stage is to lay the foundation for understanding the topic by outlining the main subjects that will be addressed during the lesson. This helps students know what to expect and focus on the specific skills they need to acquire, facilitating the assimilation of polygon concepts and their classification.

Context

 Context: To start the lesson on polygons, explain that polygons are part of our daily lives in various ways. From tile patterns on the floor, through road signs, to the shapes of buildings and artworks, polygons are geometric figures present everywhere. It is important for students to understand that learning about polygons is not just a matter of mathematical theory, but also of recognizing and understanding the world around them in a more sophisticated way.

Curiosities

 Curiosity: Did you know that the shape of bee hives is made up of regular hexagons? Bees construct their hives this way because the hexagon is the geometric shape that allows for maximum storage with minimum material, being extremely efficient and strong. This application of polygons in nature is a fascinating example of how geometry can be practical and functional.

Development

Duration: (40 - 50 minutes)

 Purpose: The aim of this stage is to provide a detailed and practical understanding of polygons, their classifications, and properties, allowing students to identify and classify polygons in different contexts. Problem-solving and practical examples help consolidate theoretical knowledge, promoting a more complete and applied learning.

Covered Topics

1.  Definition of Polygons: Explain that polygons are flat geometric figures formed by straight line segments that meet at endpoints. Each line segment is called a side, and the meeting point of two sides is called a vertex. 2.  Classification by Number of Sides: Present the types of polygons according to the number of sides: triangle (3 sides), quadrilateral (4 sides), pentagon (5 sides), hexagon (6 sides), heptagon (7 sides), octagon (8 sides), enneagon (9 sides), decagon (10 sides), and so on. 3.  Regular and Irregular Polygons: Explain that a polygon is regular when all its sides and interior angles are equal. Examples include the equilateral triangle and the square. A polygon is irregular when its sides and angles are not all equal, such as a scalene triangle or a trapezoid. 4.  Properties of Polygons: Discuss some important properties of polygons, such as the sum of the interior angles. For example, the sum of the interior angles of a triangle is always 180 degrees, while that of a quadrilateral is 360 degrees. Use the formula (n-2) * 180 degrees, where n is the number of sides, to calculate the sum of the interior angles of any polygon. 5.  Practical Examples: Provide practical and visual examples of polygons in everyday life, such as tiles, traffic signs, and architectural design. Use geometric figures and real objects to illustrate the concepts.

Classroom Questions

1. What is the sum of the interior angles of a pentagon? 2. Classify the following polygon according to the number of sides and say whether it is regular or irregular: A polygon with 5 sides, all of different lengths. 3. Give an example of a regular polygon and an example of an irregular polygon found in nature or architecture.

Questions Discussion

Duration: (20 - 25 minutes)

 Purpose: The aim of this stage is to review and consolidate the knowledge acquired by students, ensuring they fully understand the concepts discussed. The discussion of answers allows students to check their solutions and understand where they may have gone wrong, while the reflective questions stimulate critical thinking and the practical application of the learned content.

Discussion

• What is the sum of the interior angles of a pentagon? To calculate the sum of the interior angles of a pentagon, use the formula (n-2) * 180 degrees, where n is the number of sides of the polygon. In the case of the pentagon, n=5, so the sum of the interior angles is (5-2) * 180 = 3 * 180 = 540 degrees.

• Classify the following polygon according to the number of sides and say whether it is regular or irregular: A polygon with 5 sides, all of different lengths. This polygon is a pentagon since it has five sides. As all the sides are of different lengths, it is classified as an irregular pentagon.

• Give an example of a regular polygon and an example of an irregular polygon found in nature or architecture. An example of a regular polygon in nature is the hexagon found in bee hives, where all sides and angles are equal. An example of an irregular polygon in architecture can be found in some facades of modern buildings, where decorative elements may have polygon shapes with unequal sides and angles.

Student Engagement

1.  Questions and Reflections to Engage Students: 2. Why is it important to know the sum of the interior angles of a polygon? How can this be useful in geometry problems and in real life? 3. How can you quickly identify whether a polygon is regular or irregular just by looking? 4. Reflect on other examples of polygons you see daily. Which are regular and which are irregular? Why do you think they were designed that way? 5. Think of a situation where an irregular polygon would be preferable to a regular polygon. Share your ideas with the class.

Conclusion

Duration: (10 - 15 minutes)

The aim of this stage is to review and consolidate the main points discussed during the lesson, ensuring that students have a clear and comprehensive view of the content. The connection with practice and the relevance of the subject reinforce the importance of the topic, promoting meaningful and applied learning.

Summary

• Polygons are flat geometric figures formed by straight line segments that meet at endpoints.
• Classification of polygons according to the number of sides: triangle (3 sides), quadrilateral (4 sides), pentagon (5 sides), hexagon (6 sides), among others.
• Regular polygons have all sides and interior angles equal; irregular polygons have different sides and angles.
• Properties of polygons, such as the sum of the interior angles, can be calculated using the formula (n-2) * 180 degrees.
• Practical examples of polygons in daily life include tiles, traffic signs, and architectural design.

The lesson connected theory with practice by showing how polygons are present in students' everyday lives, from tile patterns to architectural shapes. This helped illustrate the applicability of theoretical concepts in real situations, facilitating comprehension and retention of the content presented.

Understanding polygons is fundamental for various areas, such as architecture, design, and even in nature. For instance, the hexagonal shape of bee hives is an example of structural efficiency. This knowledge helps students observe and analyze the world around them in a more critical and informed manner.