Lesson Plan | Technical Methodology | Angles: Vertically Opposite Angles

Objectives

Duration: 10 - 15 minutes

The purpose of this stage of the lesson plan is to ensure that students understand the fundamental concepts related to vertical angles, preparing them to apply this knowledge in solving practical problems and in real contexts. Developing these skills is essential not only for mathematical understanding but also for practical application in various professions that require geometry skills and logical reasoning.

Main Objectives

1. Identify vertical angles.

2. Understand that vertical angles are equal.

3. Solve problems using the relationship between vertical angles, such as one angle being 2x and the other x+40º.

Side Objectives

1. Develop logical and geometric reasoning skills.
2. Encourage the ability to apply theoretical concepts in practical situations.

Introduction

Duration: 10 - 15 minutes

The purpose of this stage of the lesson plan is to ensure that students understand the fundamental concepts related to vertical angles, preparing them to apply this knowledge in solving practical problems and in real contexts. Developing these skills is essential not only for mathematical understanding but also for practical application in various professions that require geometry skills and logical reasoning.

Contextualization

Vertical angles are a fundamental concept in geometry, present in various situations in our daily lives. For example, when observing the intersection of two streets or the crossing of cables on a bridge, we are dealing with vertical angles. Understanding these angles is essential not only for solving mathematical problems but also for understanding and designing various structures that we encounter daily.

Curiosities and Market Connection

Did you know that in architecture and civil engineering, understanding vertical angles is crucial to ensure the stability and safety of structures? In the job market, professionals in these fields use this knowledge to draw blueprints, calculate forces, and design buildings that can efficiently handle loads. Additionally, in robotics, these angles are used to calculate precise movements of robots, ensuring they perform tasks with high accuracy.

Initial Activity

To spark students' interest, project an image of a suspension bridge and ask: 'How do you think engineers ensure that all cables and supports are perfectly aligned and balanced?'. Then, show a short video (2-3 minutes) illustrating the application of vertical angles in bridge construction and robotics.

Development

Duration: 45 - 50 minutes

The purpose of this stage of the lesson plan is to provide students with the opportunity to apply theoretical concepts in a practical activity, promoting a deeper and more lasting understanding. Additionally, the fixation exercises help consolidate the knowledge acquired and ensure that students are able to solve problems using vertical angles.

Covered Topics

1. Definition of vertical angles
2. Property that vertical angles are equal
3. Application of vertical angles in mathematical problems
4. Practical examples from daily life and the job market

Reflections on the Theme

Guide students to reflect on how vertical angles appear in various situations in daily life and nature. Ask: 'Why is it important to understand that these angles are equal? How can this property be applied in different professions and practical problems?'

Mini Challenge

Building Bridges with Vertical Angles

Students will work in groups to build a model of a bridge using popsicle sticks and strings. They must identify and mark the vertical angles in the constructed structure.

Instructions

1. Divide the class into groups of 4 to 5 students.
2. Distribute the necessary materials (popsicle sticks, string, glue, markers).
3. Explain that each group should build a simple suspension bridge.
4. Instruct the students to identify and mark the vertical angles in their structure.
5. After construction, each group should present their bridge and explain where the vertical angles are present and how they ensure the stability of the structure.

Objective: Apply the concept of vertical angles in a practical construction, reinforcing theoretical understanding and demonstrating its relevance in real structures.

Duration: 30 - 35 minutes

Evaluation Exercises

1. Draw two pairs of intersecting lines. Identify and mark all the vertical angles.
2. Solve the equation: If one angle is 2x and its vertical angle is x + 40º, find the value of x.
3. In a street intersection, the angles formed by the streets are vertical. If one of the angles is 85º, what is the value of the opposite angle?

Conclusion

Duration: 10 - 15 minutes

The purpose of this stage of the lesson plan is to consolidate the knowledge acquired by students, connecting theory to practice and highlighting the relevance of the topic for the job market and everyday situations. This final reflection aids in lasting comprehension and appreciation of the learned concepts.

Discussion

Encourage a discussion among students about the different situations in which vertical angles appear in daily life and professions. Ask how they applied the concept during the construction of the bridge model and what challenges they faced. Encourage them to reflect on the importance of understanding these angles for solving practical problems, such as accurately calculating angles in a construction plan or ensuring that a robot executes precise movements.

Summary

Recap the main content covered in the lesson: the definition of vertical angles, the property that these angles are equal, and the application of this property in mathematical problems. Reinforce how these concepts were used in the practical bridge construction activity and in the fixation exercises.

Closing

Explain that understanding vertical angles is fundamental not only for solving mathematical problems but also for various practical applications in the job market, such as in engineering, architecture, and robotics. Emphasize that the knowledge acquired today can be applied in many daily situations, ensuring precision and efficiency in different tasks.