Lesson Plan | Technical Methodology | Sum of the Interior Angles of a Triangle

Objectives

Duration: 10 - 15 minutes

The purpose of this stage is to establish a solid foundation for students to understand the importance of recognizing and calculating the sum of the internal angles of a triangle. This knowledge is essential not only for academic mathematics but also for various practical applications in the job market, such as in engineering, architecture, and design. Focusing on the development of practical skills allows students to make deeper and lasting connections with the content, better preparing them for future educational and professional experiences.

Main Objectives

1. Recognize that the sum of the internal angles of a triangle is always 180 degrees.

2. Calculate the third angle of a triangle when the other two angles are known.

Side Objectives

1. Apply the acquired knowledge in practical and experimental situations.
2. Develop mathematical problem-solving skills.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage is to establish a solid foundation for students to understand the importance of recognizing and calculating the sum of the internal angles of a triangle. This knowledge is essential not only for academic mathematics but also for various practical applications in the job market, such as in engineering, architecture, and design. Focusing on the development of practical skills allows students to make deeper and lasting connections with the content, better preparing them for future educational and professional experiences.

Contextualization

The sum of the internal angles of a triangle is a fundamental concept in mathematics that has practical applications in various fields. Imagine engineers designing bridges, architects drawing buildings, or designers creating furniture pieces; they all rely on this basic principle to ensure that their structures are stable and functional. Knowing and applying the rule that the sum of the internal angles of a triangle is always 180 degrees is essential for any project involving geometric shapes and spaces.

Curiosities and Market Connection

️ Curiosities and Market Connection:

History: This principle was known and used by ancient civilizations like the Egyptians and the Greeks, who applied it in the construction of pyramids and temples. Application in Engineering: Civil engineers use this knowledge to calculate forces and ensure that structures like bridges and buildings are safe. Architecture: Architects rely on this property to create accurate plans and models, ensuring that all angles and dimensions are correct. Technology: Game developers and 3D animators also use these principles to create realistic virtual worlds, where geometry must be precise for the environment to function correctly.

Initial Activity

️ Initial Activity: Start the class by showing a short video that demonstrates how the sum of the internal angles of a triangle is used in the construction of a famous building, such as the Eiffel Tower. After the video, ask a provocative question: “How do you think engineers ensure that all parts of the structure are at the correct angle?”.

Development

Duration: (35 - 40 minutes)

The purpose of this stage is to deepen students' understanding of the sum of the internal angles of a triangle through practical and reflective activities. This ensures that students internalize the concept, recognizing its importance in practical contexts and developing problem-solving skills.

Covered Topics

1. Definition of internal angles of a triangle.
2. Property of the sum of the internal angles of a triangle being 180 degrees.
3. Calculation of the third angle knowing the other two angles.

Reflections on the Theme

Guide students to reflect on the importance of knowing the sum of the internal angles of a triangle in real situations. Ask how this knowledge can be applied in the construction of a bridge or in designing an architectural structure. Facilitate the discussion on the relevance of precise calculations and how they impact the safety and functionality of constructions.

Mini Challenge

Building Triangles with Sticks

Students will construct triangles using popsicle sticks and protractors to measure the angles. Then, they will calculate the sum of the internal angles and verify if the sum is equal to 180 degrees.

Instructions

1. Divide the class into groups of 3 to 4 students.
2. Distribute popsicle sticks, protractors, and graph paper to each group.
3. Instruct each group to create different types of triangles (equilateral, isosceles, and scalene).
4. Ask students to use the protractor to measure each angle of the constructed triangles.
5. Each group should record the angle values and calculate the sum of the internal angles.
6. Guide students to discuss in groups whether the sum of the internal angles corresponds to 180 degrees and to reflect on the results.

Objective: Apply the concept of the sum of the internal angles of a triangle in a practical activity, promoting comprehension and experimental verification of the theorem.

Duration: (25 - 30 minutes)

Evaluation Exercises

1. Calculate the third angle of a triangle where two angles are 45º and 85º.
2. A triangle has angles of 60º and 70º. What is the value of the third angle?
3. If a triangle has an angle of 90º and another of 30º, calculate the third angle.
4. Draw a scalene triangle and measure its angles. Check if the sum of the internal angles is 180º.

Conclusion

Duration: (15 - 20 minutes)

The purpose of this stage is to consolidate students' learning, ensuring that they have fully understood the concepts worked on and their practical applications. By promoting a discussion and recapping the contents, students can reflect on what they have learned and how it applies to the real world, reinforcing the relevance of the acquired knowledge.

Discussion

 Discussion: Facilitate a discussion where students share their reflections on the practical activity of constructing triangles and verifying the sum of the internal angles. Ask how the application of this knowledge relates to the engineering, architecture, and design activities mentioned at the beginning of the class. Encourage students to discuss the difficulties encountered and the solutions they discovered during the fixation exercises.

Summary

 Summary: Recap the main points of the lesson: the definition of internal angles of a triangle, the property that the sum of these angles is always 180 degrees, and how to calculate the third angle knowing the other two. Reinforce the importance of this knowledge both in theory and in practical applications.

Closing

 Closure: Explain how the lesson connected theory, practice, and applications. Emphasize the importance of understanding the sum of the internal angles of a triangle for various professions and everyday situations. Encourage students to continue exploring how mathematics applies in the world around them and how this knowledge can be useful in their future careers.