Lesson Plan | Teachy Methodology | Triangles: Congruence

Objectives

Duration: 10 - 15 minutes

The purpose of this stage is to clearly present the main and secondary objectives of the lesson, guiding the teacher and students regarding what is expected to be achieved by the end of the lesson. This stage establishes a solid foundation for planning activities and organizing time during the lesson.

Main Objectives

1. Understand that two congruent triangles are those that have equal angles and sides.

2. Know the main cases of triangle congruence and apply them to solve problems.

Side Objectives

1. Develop critical thinking and problem-solving skills through the application of concepts of triangle congruence.
2. Use digital tools and multimedia resources to explore and understand cases of triangle congruence.

Introduction

Duration: 10 - 15 minutes

The purpose of this stage is to engage students from the beginning of the lesson through a practical and interactive activity that uses technology with which they are already familiar. By introducing the topic in a contextualized and current manner, students are encouraged to think critically and to collaborate with each other, preparing for the deeper activities that will follow.

Warming Up

Introduce the topic of the lesson to the students in an exciting and contextualized way: 'Today, we will explore how triangles, these very common geometric shapes, can be exactly the same in some aspects, even when they look different at first glance. This is called triangle congruence! To start, ask the students to use their phones to research and share with the group an interesting or curious fact about triangles. Encourage collaboration and sharing of discoveries to enrich the beginning of the lesson.'

Initial Reflections

1. What does it mean for two triangles to be congruent?

2. What are the main criteria we can use to determine if two triangles are congruent?

3. How can triangle congruence be useful in real life or in other subjects?

4. Did anyone find a curious or surprising fact about triangles during the research? Share with the class!

Development

Duration: 70 - 80 minutes

The purpose of this stage is to provide students with an opportunity to apply and deepen their knowledge of triangle congruence in a practical and contextualized manner. Through creative activities and the use of digital technologies, students are encouraged to collaborate, communicate, and solve problems dynamically and engagingly.

Activity Suggestions

It is recommended that only one of the suggested activities be carried out

Activity 1 - Geometric Influencers 

> Duration: 60 - 70 minutes

- Objective: Students will practice explaining mathematical concepts clearly and understandably, using communication and collaboration skills.

- Description: Students will take on the role of digital math influencers. Each group will create a short video (up to 5 minutes) explaining one of the cases of triangle congruence (Side-Angle-Side; Side-Side-Side; Angle-Angle-Angle). The video will be posted on a fictional social media platform created for the lesson, where other groups can watch, comment, and evaluate the videos.

- Instructions:

• Divide students into groups of up to 5 people.

• Each group will choose (or receive) one of the cases of triangle congruence to work on.

• Groups must research and discuss among themselves to find the best way to explain the chosen case of congruence.

• Using their phones, groups must create an explanatory video of up to 5 minutes about the case of congruence.

• Videos must be posted on a platform determined by the teacher (it could be a class blog or a fictional platform).

• After posting, each group will watch the videos of the other groups and leave constructive comments and evaluations.

Activity 2 - Triangular Mission 

> Duration: 60 - 70 minutes

- Objective: Students will apply the theory of triangle congruence in practical and creative situations, developing their design and mathematical justification skills.

- Description: Students will travel on a 'space mission' where they must build bridges between different planets using congruent triangles. Using graphic design software (such as GeoGebra or a similar online tool available), students will create and demonstrate the construction of congruent triangles in various spatial contexts.

- Instructions:

• Divide students into groups of up to 5 people.

• Explain that they are on a space mission and need to build triangular bridges between planets.

• Each group will use graphic design software, such as GeoGebra, to draw congruent triangles.

• Students must decide in which spatial contexts (e.g., craters, mountains on planets) they will use the triangles and justify why congruent triangles are necessary.

• Each group must create at least three constructions and present them to the class, explaining the concepts behind their choices.

Activity 3 - Triangles in Augmented Reality ️

> Duration: 60 - 70 minutes

- Objective: Students will use augmented reality technology to consolidate their understanding of triangle congruence, applying this knowledge in an interactive and immersive way.

- Description: Using augmented reality (AR) apps, students will explore virtual environments where they need to identify and create congruent triangles. They will solve AR challenges that require applying knowledge of triangle congruence to complete specific tasks.

- Instructions:

• Divide students into groups of up to 5 people.

• Use a mobile-compatible AR application that allows the creation and manipulation of geometric shapes.

• Students will explore virtual environments provided by the app, where they need to find or create congruent triangles to advance through different levels or tasks.

• Each group must document their discoveries and strategies, sharing screenshots or short videos of their solutions.

• At the end of the activity, groups must present their main discoveries and explain how they solved the challenges.

Feedback

Duration: 15 - 20 minutes

The purpose of this stage is to reinforce learning through reflection and sharing of experiences. The group discussion allows students to consolidate their knowledge and learn from each other. The 360° feedback promotes the development of interpersonal skills, such as communication and collaboration, contributing to a more positive and productive learning environment.

Group Discussion

Promote a group discussion with all students, where groups can share their experiences and conclusions. Suggest that each group briefly present the main points of their activities, explaining the mathematical concepts addressed, the digital tools used, and the challenges faced. Use the outline below to guide the discussion:

1. Introduction: Ask each group to present the project name and a brief description of the activity.
2. Development: Request that they explain how they applied the concepts of triangle congruence and what digital tools were used.
3. Challenges and Solutions: Encourage each group to share the difficulties they encountered and how they overcame them.
4. Conclusion: Ask about the lessons learned and how the activity contributed to understanding the topic.

Reflections

1. How did the use of digital tools help to better understand triangle congruence? 2. What were the main challenges encountered during the activities and how did you resolve them? 3. In what ways could you apply the concepts learned in everyday situations or in other subjects?

360° Feedback

Conduct a 360° feedback stage, where each student should receive feedback from the other members of the group they worked with. Guide students to provide constructive and respectful feedback, using positive comments and suggestions for improvement. Explain the importance of recognizing the individual effort of each person and their contribution to teamwork. Suggest using phrases like: 'I liked how you...','You were very helpful when...','One suggestion for improvement would be...'.

Conclusion

Duration: 10 - 15 minutes

The purpose of this stage is to consolidate the knowledge acquired during the lesson in a fun and meaningful way, connecting the content covered with the real world and modern technologies. This final summary helps students reflect on the importance of what they have learned and how they can apply this knowledge in their everyday lives.

Summary

Let's take a little trip through time and space! Throughout today's lesson, we discovered that two triangles can be like identical twins (or almost!). We learned about the three magical cases of congruence: Side-Angle-Side (SAS), Side-Side-Side (SSS), and Angle-Angle-Angle (AAA). We created videos worthy of digital influencers, built triangular space bridges, and even explored augmented realities!

World Connection

In a world where everything is interconnected and increasingly digital, understanding the congruence of triangles shows us how mathematics can be present in various situations, from architectural designs to video game graphics. The use of digital tools during the lesson also prepared us for cutting-edge technologies that are shaping our future.

Practical Application

The concepts of triangle congruence help solve problems in engineering, architecture, and even in visual arts. Knowing how to identify and create congruent triangles is crucial for building stable and symmetrical structures, essential for both the physical and digital worlds.