Lesson Plan | Technical Methodology | Triangle Similarity

Objectives

Duration: 10 - 15 minutes

The purpose of this stage of the lesson plan is to establish a clear and practical foundation for understanding the criteria for triangle similarity. This is crucial for students to apply these concepts in real-life situations, whether in maker projects or in job market contexts, such as architecture and engineering. The emphasis on developing practical skills will ensure that students not only understand the theory but also know how to apply it effectively.

Main Objectives

1. Recognize the necessary and sufficient conditions for two triangles to be similar.

2. Calculate measures of angles and sides that are similar in two distinct triangles.

Side Objectives

1. Foster critical thinking and problem-solving through practical challenges.
2. Encourage collaboration among students in experimental activities.

Introduction

Duration: 15 - 20 minutes

The purpose of this stage is to engage students from the beginning by contextualizing the importance of the topic in real-life situations and in the job market. This sparks students' interest and curiosity, preparing them for the practical activities and more in-depth learning that will follow.

Contextualization

Triangles are geometric figures present in various situations in our daily lives, from bridge architecture to art and design. Understanding the similarity of triangles is fundamental for solving practical problems, such as calculating inaccessible distances or creating accurate models. This knowledge is essential not only for mathematics but also for various professions and daily activities.

Curiosities and Market Connection

 Curiosity: Did you know that the ancient Egyptians used the similarity of triangles to build the pyramids accurately? ️ Market Connection: In the job market, the similarity of triangles is crucial in fields such as civil engineering, architecture, and graphic design. For instance, engineers use these concepts to design stable and safe structures, while architects apply them to create scale models of buildings and bridges.

Initial Activity

 Initial Activity: Show a short video (2-3 minutes) about how engineers use the similarity of triangles in bridge construction. After the video, ask the following provocative question: 'How do you think we can use similar triangles to measure the height of a building without sophisticated equipment?'

Development

Duration: 55 - 65 minutes

The purpose of this stage of the lesson plan is to deepen students' understanding of triangle similarity through practical and interactive activities. This will consolidate the theoretical concepts previously presented and demonstrate their applications in real situations. In addition, the fixation and assessment exercises will allow students to practice and validate their understanding, ensuring a more effective and meaningful learning experience.

Covered Topics

1. Necessary and sufficient conditions for two triangles to be similar.
2. Criteria for triangle similarity: AA (angle-angle), LAL (side-angle-side), LLL (side-side-side).
3. Calculation of measures of angles and sides in similar triangles.
4. Practical applications of triangle similarity in real and professional contexts.

Reflections on the Theme

Guide students to reflect on how the similarity of triangles can be applied in their everyday lives and future careers. Ask them about situations where they might have seen or used similar triangles without realizing it, like in construction games, art projects, or even observing the architecture around them. Encourage them to think about the importance of understanding these geometric relationships to solve practical problems and create innovative solutions.

Mini Challenge

Maker Challenge: Building a Simple Theodolite

Students will build a simple theodolite using accessible materials and then use it to measure the height of a tall object, such as a tree or a building. This practical activity connects the theory of triangle similarity with a real application in the field of engineering and architecture.

Instructions

1. Divide the students into small groups and distribute the necessary materials: protractors, straws, tape, string, and weights (like paper clips).
2. Instruct the students to attach a straw to the edge of the protractor using tape, so they can look through the straw and read the angle on the protractor.
3. Ask them to attach a piece of string to the center of the protractor, with a weight at the end, to serve as a plumb line.
4. Take the students outside the classroom and choose a tall object to measure.
5. Guide the students to look through the straw at the top of the object and read the angle on the protractor while keeping the plumb line aligned with the vertical.
6. Students should record the measured angle and the distance from the observation point to the base of the object.
7. Using the relationships of triangle similarity, the students will calculate the height of the measured object.

Objective: Apply the concepts of triangle similarity in a practical activity and develop measurement and calculation skills in a real context.

Duration: 30 - 40 minutes

Evaluation Exercises

1. Solve the following triangle similarity problems: Determine the height of a building knowing that the shadow of a person 1.80 m tall casts a shadow of 2 m, and the shadow of the building measures 20 m. Two triangles are similar. In the first triangle, the sides are 3 cm, 4 cm, and 5 cm. The longest side of the second triangle measures 15 cm. Calculate the other two sides of the second triangle.
2. Ask students to draw two similar triangles and identify all corresponding angles and sides. Then, swap drawings with a peer and check each other's answers.

Conclusion

Duration: 10 - 15 minutes

The purpose of this stage of the lesson plan is to consolidate students' learning by reinforcing the main concepts discussed and the practical skills developed. Through recap and discussion, students will be able to reflect on the importance of the topic and its application in real situations, strengthening their understanding and the relevance of the knowledge acquired.

Discussion

 Discussion: Promote an open discussion about how triangle similarity was addressed during the lesson. Ask students how they felt building the theodolite and measuring the height of an object, and how this practical experience helped in understanding theoretical concepts. Encourage them to share insights about the challenges faced and the solutions found, as well as to discuss the practical applications of the knowledge gained.

Summary

 Summary: Recap the main content covered in the lesson, emphasizing the criteria for triangle similarity (AA, LAL, LLL) and the importance of recognizing the conditions for two triangles to be similar. Remind them how to calculate measures of angles and sides in similar triangles and highlight the practical applications discussed, such as in the construction of structures and height measurement.

Closing

 Closing: Explain how the lesson connected theory with practice through the construction of the theodolite and the measurement of a real object. Reinforce the importance of triangle similarity in everyday life and in various professions, such as engineering, architecture, and graphic design. Emphasize that understanding these concepts allows for solving practical problems and innovating in different contexts.