Lesson Plan | Traditional Methodology | Internal Angles of Quadrilaterals

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage is to introduce students to the concept of internal angles of quadrilaterals and to show the relevance of the sum of the internal angles being 360º. This understanding is fundamental for solving problems related to quadrilaterals, allowing students to calculate missing angles based on known angles. The goal is to create a solid foundation so they can apply this knowledge in practical exercises and future contexts.

Main Objectives

1. Teach students that the sum of the internal angles of a quadrilateral is always 360º.

2. Demonstrate how to calculate a missing angle in a quadrilateral when three internal angles are known.

3. Provide practical and guided examples to reinforce understanding of the concept.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage is to introduce students to the concept of internal angles of quadrilaterals and to show the relevance of the sum of the internal angles being 360º. This understanding is fundamental for solving problems related to quadrilaterals, allowing students to calculate missing angles based on known angles. The goal is to create a solid foundation so they can apply this knowledge in practical exercises and future contexts.

Context

To start the lesson on the internal angles of quadrilaterals, explain to the students that quadrilaterals are geometric figures with four sides and four angles. Common examples of quadrilaterals are the square, rectangle, parallelogram, and trapezoid. Highlight that understanding the sum of the internal angles of these figures is essential for solving geometry problems and better understanding the world around us, such as in civil construction, engineering, and even art.

Curiosities

Did you know that architects use the knowledge of the internal angles of quadrilaterals when designing houses and buildings? For example, when drawing the layout of a rectangular room, they need to ensure that all internal angles add up to 360º so that the room has the correct shape. Additionally, in video games, designers use quadrilaterals to create 3D environments, ensuring that all internal angles are correct to provide a realistic visual experience.

Development

Duration: (50 - 60 minutes)

The purpose of this stage is to deepen students' understanding of the internal angles of quadrilaterals by offering detailed explanations and practical examples. The goal is to ensure that students are capable of calculating missing angles in quadrilaterals and applying this knowledge in solving geometric problems and in real-world contexts.

Covered Topics

1. Definition of Quadrilaterals: Explain that a quadrilateral is a geometric figure with four sides and four angles. Provide examples of common quadrilaterals such as square, rectangle, parallelogram, and trapezoid. 2. Sum of Internal Angles: Highlight that the sum of the internal angles of any quadrilateral is always 360º. Show the formula for the sum of internal angles, which is (n-2) * 180º, where n is the number of sides. For quadrilaterals, substituting n with 4, the sum is 360º. 3. Calculation of Missing Angle: Demonstrate how to calculate a missing angle in a quadrilateral when three internal angles are known. Use practical examples to illustrate the process, such as: if the known angles are 30º, 70º, and 50º, calculate the fourth angle. The sum of the three angles is 150º, so the missing angle is 360º - 150º = 210º. 4. Problem Solving: Guide students in solving practical problems, providing additional examples and explaining each step in detail. Encourage students to note down solutions and practice with other examples. 5. Practical Applications: Explain how the knowledge of internal angles of quadrilaterals is used in practical areas such as architecture, engineering, and video game design. Reinforce the importance of the concept in real life.

Classroom Questions

1. Given a quadrilateral with internal angles of 90º, 85º, and 95º, calculate the missing angle. 2. If a quadrilateral has internal angles of 120º, 100º, and 90º, what is the value of the fourth angle? 3. A quadrilateral has three known angles: 60º, 80º, and 110º. What is the value of the remaining angle?

Questions Discussion

Duration: (15 - 20 minutes)

The purpose of this stage is to review the explanations for the questions solved by the students, ensuring that everyone understands the concepts and the necessary steps to calculate the missing angles in quadrilaterals. Additionally, this stage allows for engaging students in reflective discussion, reinforcing learning, and demonstrating the practical application of the concept.

Discussion

• For the question with internal angles of 90º, 85º, and 95º, start by adding these angles: 90º + 85º + 95º = 270º. To find the missing angle, subtract this sum from 360º: 360º - 270º = 90º. Therefore, the missing angle is 90º.

• In the question where the internal angles are 120º, 100º, and 90º, add these angles first: 120º + 100º + 90º = 310º. Subtract this sum from 360º to find the missing angle: 360º - 310º = 50º. Thus, the missing angle is 50º.

• For the quadrilateral with internal angles of 60º, 80º, and 110º, add the angles: 60º + 80º + 110º = 250º. Subtract this sum from 360º to find the remaining angle: 360º - 250º = 110º. The remaining angle is therefore 110º.

Student Engagement

1. Ask students: 'What steps did you follow to find the missing angles?' 2. Question: 'Why is it important to know that the sum of the internal angles of a quadrilateral is 360º?' 3. Ask them to reflect: 'In what other everyday situations do you think this knowledge about internal angles could be useful?' 4. Encourage discussion on practical application: 'Can someone give an example of how the internal angles of quadrilaterals are used in architecture or video game design?'

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to summarize and reinforce the main content presented during the lesson, ensuring that students understand and retain the information. It also aims to connect theory to practice and highlight the importance of the topic in the daily lives of students, consolidating learning in a meaningful way.

Summary

• Quadrilaterals are geometric figures with four sides and four angles.
• The sum of the internal angles of any quadrilateral is always 360º.
• To calculate the missing angle in a quadrilateral, subtract the sum of the known angles from 360º.
• Practical examples were provided to illustrate the calculation of missing angles.
• The application of knowledge about the internal angles of quadrilaterals is relevant in fields like architecture, engineering, and video game design.

The lesson connected the theory of the internal angles of quadrilaterals with practice by providing detailed, guided examples for calculating missing angles. Furthermore, the practical applications of this knowledge in various fields such as architecture and video game design were discussed, highlighting its relevance in the real world.

Knowledge of the internal angles of quadrilaterals is important for various everyday situations, such as in civil construction and the design of virtual environments. For example, architects need to ensure that the angles of a room add up to 360º for the construction to be correct. Additionally, video game designers use the same principle to create realistic 3D environments.