LESSON PLAN 5
- Symmetry all around us
- Arts (includes music, architecture ...), ICT (includes technical education, computer science ...), Mathematics (includes geometry, proportionality, finances ...), Other (social studies, geography,,,), Science (includes physics, biology ...)
- ISCED 2 = Lower Secondary Education
Duration
3 and a half hours / 4 activities / 50 minutes each
Topic
Applying symmetry around us by making images with symmetrical figures, symmetrical constructions from various material and digital resources.
Synopsis
Recognizing the importance and applicability of symmetry in our everyday life. The application of studied geometric transformations (symmetry against a point, symmetry against a straight line) to identify and explain phenomena, processes.
Contributors
Parents who are engineers, scientists…, teachers from other related subjects (NS, ICT, Arts…)
Framework
Teacher’s cooperation and division of work:
The mathematics teacher has the responsibility to identify and deliver the subject, to promote, to help, to organize the whole learning procedure
- Task 1: Establishing the relationship with previous experience, updating knowledge and capabilities/skills.
Students watch a video presentation, give examples of symmetric objects and define the basic notions.
- Task 2: Research the topic (Symmetry) to present it to peers in an attractive way.
- Task 3: Discussion for understanding, articulating hypotheses, making generalizations, correcting errors.
The students, organized in groups (3-4), are working with one of the following tools: GEOGEBRA, PAINT 3D, GEOBOARD, SYMMETRICAL paper applications.
- Task 4: Presentation of results, application of acquired knowledge in various real and/or modeled situations, application of another approach.
Students organize themselves in workshops and work individually or in pairs on one of the proposed themes (according to theirs own abilities): MATHEMATICS WORKSHOP, PAINTING WORKSHOP, PROGRAMMER’S WORKSHOP, HISTORY WORKSHOP, THE PHYSICIAN’S WORKSHOP, BUILDERS’ WORKSHOP.
- Task 5: Evaluation of operation mode, progress, products made, correction of mistakes.
Reflection (Conclusion).
Material / Equipment
Material resources: interactive whiteboard, projector, calculator, worksheets, colored sheets, scissors, digital tools, Lego figures, etc.
Informational and methodological resources: Padlet.com, Geogebra, Canva.com,
Storyjumper.com, Wordwall.com, Kahoot.com, Learningapps.com, Padlet.com,
Zoom
Previous knowledge and skills
This project does not require previous knowledge related to the topic addressed. The documentation will be done during the development of the project.
Learning Objectives
Learning goals and objectives:
At the end of the project, the student will be able to:
- recognize the importance and applicability of symmetry in our daily life;
- apply the studied geometric transformations to identify and explain phenomena, processes;
- apply the studied digital tools to the creation of images with elements of everyday symmetry;
- evaluate the performances achieved in the project;
- develop communication and collaboration skills.
Learning outcomes and expected outcomes:
The project “Symmetry around us” aims to develop the skills:
- capitalizing on theoretical knowledge in practical contexts, demonstrating what they know to do and what the students know to be;
- knowledge transfer in problem solving;
- critical approach and processing of accumulated information;
- communication and collaboration;
- effective application of IT tools
Methodology
Information stage:
Students get acquainted with the basic notions:
There are given examples of objects, bodies, etc… in which it is put in highlight the symmetry.
Students define the notions of: congruent figures, axis of symmetry, symmetrical figures and asymmetrical figures.
Word wall game:
SYMMETRYhttps://wordwall.net/play/10023/492/989
It is mentioned that the assignment of students to workshops and their activity was carried out according to each student’s own desire, and their individual capacities were also taken into account according to the results of the S. Dellinger psycho geometric testing.
Preparation & Resources
Preparation, Space Setting, Troubleshooting Tips:
– Presentation of each member of the project in Padlet (the avatar, a small description of each member)
Activity 1. – Students will investigate what symmetry is, where it is applied around us, which of the scientists discovered symmetry, what they know about those discoveries, they will take photos of images with symmetrical elements from around us, they will post and write in Padlet.
Resources, Tools, Material, Attachments, Equipment
There are instructions available online, which explain how this can be done effectively, e.g., https://www.youtube.com/watch?v=kKLga-8IMiY
Inspirations for symmetry in the literature can be found here: https://www.sciencedirect.com/science/article/pii/0898122186901513
Symmetries in music are considered here: http://www.mi.sanu.ac.rs/vismath/visbook/apagyi/index.html
Nice introduction to symmetry in the architecture, already organized in form of a lesson is available here: http://www.mi.sanu.ac.rs/vismath/visbook/apagyi/index.html
Additional material is presented here:
Implementation
The implementation stage:
Students are divided into teams of 3-4 students each. The students organize into groups and work on one of the applications suggested. Students can apply to the other exercises as well.
I. GEOGEBRA application:
Students will draw the symmetry of the pink figure in relation to the blue axis.
https://www.geogebra.org/classic/m4yv2zpb
II. The PAINT 3D application:
Students will build symmetrical drawings in the Paint 3D Application.
https://sites.google.com/stefan-voda.clasaviitorului.md/steam/explicarea/2
III. The GEOBOARD application
Students will make symmetrical pictures in the Geoboard application.
https://apps.mathlearningcenter.org/geoboard/?32rec9k2
IV. SYMMETRICAL applications
Students will make “Positive & Negative” paper applications.
Instructions: Use 2 sheets of contrasting colored paper, for example black and white.
Cut the white sheet vertically. Make a drawing at desire. Cut out the drawing and paste on the whole sheet of paper so you get a symmetrical application.
Students’ works are added to the digital board:
https://padlet.com/galina_popesco/y8sfsplgssdk4yx
The stage of presentation of the final products of the project and their evaluation:
Students organize themselves in workshops and work individually or in pairs on one of the proposed themes. The products are place on the digital board:
https://padlet.com/galina_popesco/v84d2av5g1k34jd3
WORKSHOP:
MATHEMATICS WORKSHOP:
The students will work on sheets in which they will have to build the axis of symmetry of an isosceles and equilateral triangle. The properties of geometric figures will be noticed. They will also build the axis of symmetry of the letters in the word STEAM. (Appendix 1)
PAINTING WORKSHOP:
Students will draw a painting based on the symmetry called MANDALA. Their works will be displayed at a school exhibition. (Appendix 2)
PROGRAMMER’S WORKSHOP:
Students will write code programs for geometric constructions, of the axis of symmetry and the construction of the MANDALA drawing. (Appendix 3)
HISTORY WORKSHOP:
Students, using the Internet, will look for countries whose flags admit axis of symmetry.
THE PHYSICIAN’S WORKSHOP:
Students will make a quarter or half an application. With the help of mirrors they will highlight the role of reflection in symmetry. Examples of photos with reflections from the nature will be brought.
BUILDERS’ WORKSHOP
Students will make a symmetrical construction from lego pieces.
Outline of the Lesson
Extension Activities
Students who progress faster can optionally try to draw the graph of inverse functions (e.g. quadratic function vs. radical function). For students with some kind of disability development, a worksheet suitable to the student’s abilities has been prepared.
Assessmement
Questionnaire for self-assessment activity
Activity balance
1.Name an object from around us which admit axis of symmetry
- At the lesson today I liked …
- I felt …
- I am satisfied with …
- Next time I want to participate in the workshop …
https://www.menti.com/v6d9o5agp7
As a result, students are involved in authentic, meaningful learning situations, develop critical and self-critical thinking, encourage innovation, develop the ability to collaborate and communicate effectively, increase students motivation to learn.
The strong points of the activity consist in: arguing and valorizing one’s own ideas, opinions; the development of the student’s critical and self-critical thinking; developing the capacity for understanding, collaboration and communication; the formation of mathematical, digital and linguistic skills.
The weak points of this activity are: lack of teaching support; the need for more time allocated for such activities.
Conclusions: Active learning involves effective didactic strategies, by capitalizing on mathematical skills. The student becomes responsible in selecting and managing the learning path, which contributes to the development of his own personality. Students are much more motivated if subjects are taught from diverse perspectives, and if they are based on facts from everyday life, when the strongest argument is the very fact that life is not divided into disciplines.
References
https://pinnguaq.com/learn/math-in-nature-video-series/math-in-nature-part-1/; https://www.youtube.com/watch?v=FYjIW_bJWcQ
https://ibn.idsi.md/sites/default/files/imag_file/p-294-300.pdf;
http://gimnaziulcornesti.educ.md/2021/10/20/cum-sa-organizam-activitati-practice-proiecte-de-tipul-stem-steam-lucrari-de-laborator-in-cadrul-procesului-educational-la-matematica-in-gimnaziu-si-liceu/