Lesson Plan | Active Learning | Symmetry in Relation to Axes

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5 - 10 minutes)

The Objectives stage is crucial for establishing a solid foundation for the rest of the lesson. By clearly defining what is expected for students to learn, this section guides the entire teaching and learning process, ensuring that both the teacher and the students are aligned with the pedagogical goals. This stage also serves to motivate students by demonstrating the relevance of the topics covered in practical and theoretical situations of everyday life.

Main Objectives:

1. Empower students to recognize symmetrical figures and identify their axes of symmetry, including determining the number of axes.

2. Develop the ability to calculate distances from points to symmetric axes or symmetry points in symmetrical figures.

3. Ensure understanding of the concept of reflective symmetry and its application in various geometric figures.

Side Objectives:

1. Encourage the application of mathematical concepts in everyday situations through practical examples during in-class activities.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to engage students with the content they studied previously at home, through problem situations that stimulate critical thinking and the direct application of the concept of symmetry in practical and real situations. Additionally, by contextualizing the importance of symmetry in everyday life, it awakens students' interest, showing them the relevance of the topic in the world around them before diving into practical activities in class.

Problem-Based Situations

1. Ask students to analyze a drawing where one half is filled and the other half is blank. They should identify the axis of symmetry that would divide the drawing into two identical parts.

2. Show a map of a city where some tourist points are located symmetrically relative to an axis not shown on the map. Ask students to identify the line of symmetry and calculate the distance from a given point to the axis.

Contextualization

Explain that symmetry is present in many aspects of our daily lives, from drawings and art to the organization of objects in environments. Symmetry is a powerful tool in mathematics and art, allowing for the creation of aesthetically pleasing patterns and facilitating the resolution of geometric and design problems. Furthermore, symmetry is a fundamental concept in various cultures, often used in symbols and architectural structures.

Development

Duration: (70 - 75 minutes)

The Development section is designed to allow students to apply the concepts of symmetry learned in a practical and creative way. Through group activities, they will have the opportunity to explore symmetry in various contexts, from art to applied mathematics. These activities not only solidify students' theoretical understanding but also encourage collaboration and critical thinking. Each proposed activity aims to achieve specific objectives, such as identifying axes of symmetry, creating symmetrical figures, and applying symmetry in practical situations, ensuring a holistic and engaging learning experience.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - Symmetrical Art: Creating Mandalas

> Duration: (60 - 70 minutes)

- Objective: Develop visual perception and the ability to draw symmetrical figures, as well as to identify axes of symmetry in complex figures.

- Description: In this activity, students will create mandalas using paper, colored pencils, and a ruler. They must design a symmetrical mandala by drawing a sector and replicating it around an axis of symmetry. The final mandala must present at least 4 axes of symmetry.

- Instructions:

• Divide the class into groups of up to 5 students.

• Distribute kits of papers, colored pencils, and ruler to each group.

• Explain the concept of mandalas and show examples of mandalas with multiple axes of symmetry.

• Ask students to draw the sector of their mandala in one of the quadrants of the paper, respecting the symmetry.

• Students should then copy and rotate the drawn sector in the other three quadrants to complete the mandala.

• Guide students to identify and mark the axes of symmetry used.

• Each group presents their mandala to the class, explaining the identified axes of symmetry and the drawing process.

Activity 2 - Symmetry Detectives

> Duration: (60 - 70 minutes)

- Objective: Enhance the ability to identify symmetries in everyday objects and reinforce understanding of axes of symmetry.

- Description: Students will become 'detectives' who need to find and identify symmetrical objects in a 'crime scene.' The room will be decorated with various objects that have symmetry and some that do not. Each group will receive a list of symmetrical objects to find and will describe the axis of symmetry of each object.

- Instructions:

• Prepare the room with a variety of objects that have or do not have symmetry.

• Organize students into groups and distribute the list of objects to search for.

• Each group must circle the symmetrical objects found and describe the axis of symmetry of each one.

• Allow students to use adhesive tape or markers to visually mark the axes of symmetry on the objects.

• At the end, each group presents their findings and explains the observed axes of symmetry.

Activity 3 - Constructors of Symmetrical Cities

> Duration: (60 - 70 minutes)

- Objective: Apply the concept of symmetry in an urban planning context, developing drawing and planning skills.

- Description: Students will design a part of a city where buildings and streets must be arranged symmetrically in relation to an axis. Using grid paper, pencils, and erasers, they will draw a map that includes at least two buildings and one street, all symmetrically arranged.

- Instructions:

• Divide students into groups and provide grid paper, pencils, and erasers.

• Explain how symmetry can be applied in architecture and urban planning.

• Students should draw a building in the middle of a quadrant, using symmetry to replicate it in the other quadrants.

• Then, they draw a street that acts as an axis of symmetry for new buildings.

• Each group presents their project, explaining the use of symmetry and the chosen axis of symmetry.

Feedback

Duration: (15 - 20 minutes)

The purpose of this stage is to consolidate learning, allowing students to articulate what they have learned and reflect on the practical application of symmetry. The group discussion helps reinforce understanding of the concepts of symmetry and axes of symmetry, in addition to promoting communication and argumentation skills. This feedback also allows the teacher to assess how well students understood the content and identify areas that may need additional review.

Group Discussion

To start the group discussion, the teacher can ask each group to share a brief reflection on what they learned during the activities. Suggest that each group discuss the difficulties encountered, how they overcame those challenges, and what they found most interesting about the application of symmetry in the different contexts. This moment serves for students to verbalize the knowledge acquired and hear perspectives of their peers, enriching the understanding of the theme.

Key Questions

1. What were the biggest challenges in identifying axes of symmetry in the proposed activities?

2. How can symmetry be applied in other areas besides mathematics, such as in art or architecture?

3. Why is it important to understand and recognize symmetry in everyday objects?

Conclusion

Duration: (5 - 10 minutes)

The Conclusion stage is essential to consolidate learning and ensure that students have a clear and integrated understanding of the concepts covered. Additionally, it serves to reinforce the relevance and applicability of studying symmetry in practical and theoretical situations. This stage helps students relate mathematical knowledge to the world around them and value mathematics as an essential tool in developing analytical and critical skills.

Summary

At this final moment, the teacher should summarize the main concepts covered, such as identifying symmetrical figures, their axes of symmetry, and the application of reflective symmetry. It should be emphasized how axes of symmetry are essential for dividing figures into equal parts and how students applied these concepts in practical activities.

Theory Connection

The teacher should explain how today's lesson connected theory and practice, demonstrating the applicability of symmetry concepts in real and practical contexts, such as in creating mandalas, analyzing maps, and urban art. Highlight the importance of understanding symmetry not only as a mathematical concept but as a tool that can be used in various everyday situations and in other disciplines.

Closing

Finally, it is essential for the teacher to discuss the relevance of studying symmetry for the students' daily lives, highlighting how this knowledge can be applied in their lives, either in solving practical problems or in appreciating aesthetic and symmetrical design. This moment also serves to motivate students, showing the importance and beauty of mathematics in real and tangible situations.