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Ideas for using GeoGebra and Origami in Teaching Regular Polyhedrons Lessons

2018

The approach of combining GeoGebra and origami is well accepted among students in the school "Petro Kuzmjak" where it is used to teach geometry lessons. This article elaborates on how to introduce students (upper elementary and high school students, age 14-18) to Platonic solids and their properties through combination of GeoGebra and origami activities. Some of the important mathematical concepts related to these well-known geometrical solids can be explained to students applying hands-on activities along with educational software. peerReviewed

origamitoppitunnithands-on activities05 social sciences050301 educationGeogebra Origami Platonic solids hands-on activities geometry lessonsgeometry lessonsOrigamilcsh:Education (General)kiinteät aineetGeoGebraGeogebraorigami0502 economics and businessgeometrialcsh:Llcsh:L7-9910503 education050203 business & managementlcsh:EducationPlatonic solids

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PEPhysical Sciences and Engineering
- PE2Fundamental Constituents of Matter
  - PE2_1Theory of fundamental interactions
  - PE2_2 Phenomenology of fundamental interactions
  - PE2_3Experimental particle physics with accelerators
  - PE2_4Experimental particle physics without accelerators
  - PE2_6Nuclear, hadron and heavy ion physics
  - PE2_8Gas and plasma physics
  - PE2_5Classical and quantum physics of gravitational interactions
  - PE2_7Nuclear and particle astrophysics
  - PE2_9 Electromagnetism
  - PE2_10Atomic, molecular physics
  - PE2_11Ultra-cold atoms and molecules
  - PE2_18Equilibrium and non-equilibrium statistical mechanics: steady states and dynamics
  - PE2_14Lasers, ultra-short lasers and laser physics
  - PE2_17Metrology and measurement
  - PE2_16Non-linear physics
  - PE2_12Optics, non-linear optics and nano-optics
  - PE2_13Quantum optics and quantum information
  - PE2_15Thermodynamics
- PE1Mathematics
  - PE1_1Logic and foundations
  - PE1_6Geometry and global analysis
  - PE1_8Analysis
  - PE1_7Topology
  - PE1_9Operator algebras and functional analysis
  - PE1_10ODE and dynamical systems
  - PE1_12Mathematical physics
  - PE1_11Theoretical aspects of partial differential equations
  - PE1_13Probability
  - PE1_14Mathematical statistics
  - PE1_15Generic statistical methodology and modelling
  - PE1_4 Algebraic and complex geometry
  - PE1_19Scientific computing and data processing
  - PE1_2Algebra
  - PE1_20Control theory, optimisation and operational research
  - PE1_21Application of mathematics in sciences
  - PE1_22Application of mathematics in industry and society
  - PE1_5Lie groups, Lie algebras
  - PE1_18Numerical analysis
  - PE1_16Discrete mathematics and combinatorics
  - PE1_17Mathematical aspects of computer science
  - PE1_3Number theory
- PE3Condensed Matter Physics
  - PE3_1Structure of solids, material growth and characterisation
  - PE3_2Mechanical and acoustical properties of condensed matter, lattice dynamics
  - PE3_3Transport properties of condensed matter
  - PE3_4Electronic properties of materials, surfaces, interfaces, nanostructures
  - PE3_6Macroscopic quantum phenomena, e.g. superconductivity, superfluidity, quantum Hall effect
  - PE3_5Physical properties of semiconductors and insulators
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  - PE3_14Fluid dynamics (physics)
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  - PE5_12Chemistry of condensed matter
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  - PE5_7Biomaterials synthesis
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  - PE4_2Spectroscopic and spectrometric techniques
  - PE4_3Molecular architecture and Structure
  - PE4_1Physical chemistry
  - PE4_4Surface science and nanostructures
  - PE4_5Analytical chemistry
  - PE4_6Chemical physics
  - PE4_7Chemical instrumentation
  - PE4_8Electrochemistry, electrodialysis, microfluidics, sensors
  - PE4_10Heterogeneous catalysis
  - PE4_9Method development in chemistry
  - PE4_11Physical chemistry of biological systems
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- PE10Earth System Science
  - PE10_2Meteorology, atmospheric physics and dynamics
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  - PE10_8Oceanography (physical, chemical, biological, geological)
  - PE10_1Atmospheric chemistry, atmospheric composition, air pollution
  - PE10_4Terrestrial ecology, land cover change
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  - PE10_16Ozone, upper atmosphere, ionosphere
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  - PE10_17Hydrology, hydrogeology, engineering and environmental geology, water and soil pollution
  - PE10_18Cryosphere, dynamics of snow and ice cover, sea ice, permafrosts and ice sheets
  - PE10_20Geohazards
  - PE10_19Planetary geology and geophysics
  - PE10_21Earth system modelling and interactions
  - PE10_14Earth observations from space/remote sensing
  - PE10_11Geochemistry, cosmochemistry, crystal chemistry, isotope geochemistry, thermodynamics
  - PE10_13Physical geography, geomorphology
  - PE10_12Sedimentology, soil science, palaeontology, earth evolution
- PE11Materials Engineering
  - PE11_2Engineering of metals and alloys
  - PE11_1Engineering of biomaterials, biomimetic, bioinspired and bio-enabled materials
  - PE11_3Engineering of ceramics and glasses
  - PE11_4Engineering of polymers and plastics
  - PE11_5Engineering of composites and hybrid materials
  - PE11_6Engineering of carbon materials
  - PE11_7Engineering of metal oxides
  - PE11_8Engineering of alternative established or emergent materials
  - PE11_9Nanomaterials engineering, e.g. nanoparticles, nanoporous materials, 1D & 2D nanomaterials
  - PE11_10Soft materials engineering, e.g. gels, foams, colloids
  - PE11_11Porous materials engineering, e.g. covalent-organic, metal-organic, porous aromatic frameworks
  - PE11_12Semi-conducting and magnetic materials engineering
  - PE11_13Metamaterials engineering
  - PE11_14Computational methods for materials engineering
LSLife Sciences
- LS1Molecules of Life: Biological Mechanisms, Structures and Functions
  - LS1_2Biochemistry
  - LS1_1Macromolecular complexes including interactions involving nucleic acids, proteins, lipids and carbohydrates
  - LS1_3DNA and RNA biology
  - LS1_4Protein biology
  - LS1_5Lipid biology
  - LS1_6Glycobiology
  - LS1_11Chemical biology
  - LS1_12Protein design
  - LS1_13Early translational research and drug design
  - LS1_14Innovative methods and modelling in molecular, structural and synthetic biology
  - LS1_10Synthetic biology
  - LS1_8Structural biology
  - LS1_9Molecular mechanisms of signalling processes
  - LS1_7Molecular biophysics, biomechanics, bioenergetics
- LS2Integrative Biology: from Genes and Genomes to Systems
  - LS2_1Genetics
  - LS2_3Epigenetics
  - LS2_2Gene editing
  - LS2_4Gene regulation
  - LS2_5Genomics
  - LS2_6Metagenomics
  - LS2_7Transcriptomics
  - LS2_8Proteomics
  - LS2_9Metabolomics
  - LS2_10Glycomics/Lipidomics
  - LS2_11Bioinformatics and computational biology
  - LS2_12Biostatistics
  - LS2_14Genetic diseases
  - LS2_16Innovative methods and modelling in integrative biology
  - LS2_13Systems biology
  - LS2_15Integrative biology for personalised medicine
- LS4Physiology in Health, Disease and Ageing
  - LS4_1Organ and tissue physiology and pathophysiology
  - LS4_4Endocrinology
  - LS4_3Physiology of ageing
  - LS4_2Comparative physiology
  - LS4_5Non-hormonal mechanisms of inter-organ and tissue communication
  - LS4_6Microbiome and host physiology
  - LS4_7Nutrition and exercise physiology
  - LS4_8Impact of stress (including environmental stress) on physiology
  - LS4_9Metabolism and metabolic disorders, including diabetes and obesity
  - LS4_10The cardiovascular system and cardiovascular diseases
  - LS4_11Haematopoiesis and blood diseases
  - LS4_12Cancer
  - LS4_13Other non-communicable diseases (except disorders of the nervous system and immunity-related diseases)
- LS3Cell Biology, Development, Stem Cells and Regeneration
  - LS3_4Cell junctions, cell adhesion, the extracellular matrix, cell communication
  - LS3_5Cell signalling and signal transduction, exosome biology
  - LS3_6Organelle biology and trafficking
  - LS3_7Mechanobiology of cells, tissues and organs
  - LS3_8Embryogenesis, pattern formation, morphogenesis
  - LS3_9Cell differentiation, formation of tissues and organs
  - LS3_10Developmental genetics
  - LS3_11Evolution of developmental strategies
  - LS3_12Organoids
  - LS3_3Cell behaviour, including control of cell shape, cell migration
  - LS3_13Stem cells
  - LS3_14Regeneration
  - LS3_15Development of cell-based therapeutic approaches for tissue regeneration
  - LS3_17Theoretical modelling in cellular, developmental and regenerative biology
  - LS3_16Functional imaging of cells and tissues
  - LS3_1Cell cycle, cell division and growth
  - LS3_2Cell senescence, cell death, autophagy, cell ageing
- LS5Neuroscience and Disorders of the Nervous System
  - LS5_1Neuronal cells
  - LS5_3Neural development and related disorders
  - LS5_5Neural networks and plasticity
  - LS5_10Ageing of the nervous system
  - LS5_11Neurological and neurodegenerative disorders
  - LS5_12Mental disorders
  - LS5_7Sensory systems, sensation and perception, including pain
  - LS5_13Nervous system injuries and trauma, stroke
  - LS5_14Repair and regeneration of the nervous system
  - LS5_15Neuroimmunology, neuroinflammation
  - LS5_16Systems and computational neuroscience (e.g. modelling, simulation, brain oscillations, connectomics)
  - LS5_18Innovative methods and tools for neuroscience
  - LS5_17Imaging in neuroscience
  - LS5_9Neural basis of cognition (e.g. learning, memory, attention, emotions, speech)
  - LS5_6Neurovascular biology and blood-brain barrier
  - LS5_8Neural basis of behaviour (e.g. sleep, consciousness, addiction)
  - LS5_4Neural stem cells
  - LS5_2Glial cells and neuronal-glial communication
- LS6Immunity, Infection and Immunotherapy
  - LS6_1Innate immunity
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  - LS6_3Regulation of the immune response
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  - LS6_5Biology of pathogens (e.g. bacteria, viruses, parasites, fungi)
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  - LS6_8Biological basis of prevention and treatment of infection
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  - LS7_8Effectiveness of interventions, including resistance to therapies
  - LS7_9Public health and epidemiology
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  - LS9_1Bioengineering for synthetic and chemical biology
SHSocial Sciences and Humanities
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  - SH8_8Visual and performing arts, screen, arts-based research
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