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Fractions - Parts of a Whole: Visual Models

Fractions - Parts of a Whole: Visual Models
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2019-06-11 03:15
CircleSequenceGeometric ConstructionSlider Animation
In collections Fraction Book
This GeoGebra example demonstrates the meaning of fractions using different geometric models, showing how a whole is divided into equal parts and how each part relates to the whole. The core mathematical concepts include the definition of fractions, equal partitioning, part-whole relationships, and the correspondence between fractions and geometric shapes. The construction uses commands such as Circle to create the whole, OrthogonalLine and Intersect to construct dividing lines, Sequence and Element to generate multiple wedge sectors, and Segment to connect key points. Key objects include NumberOfParts to control the number of divisions, WedgeSize and WedgeDots to adjust display details, multiple wedge objects (Wedge01 to Wedge20) representing different fractional parts, and colorchanger objects for dynamic coloring. This resource is suitable for upper elementary and middle school students learning fractions, and for teachers to use in classroom demonstrations to help students visually grasp the meaning of numerators and denominators.

GeoGebra Commands & Parameters

  1. Circle(A, radius) → c
  2. OrthogonalLine(A, xAxis) → f
  3. Intersect(c, f, 2) → B
  4. Sequence(Rotate[B, (WedgeSize° * i), A], i, 0, NumberOfParts) → WedgeDots
  5. Sequence(CircleSector[A, Element[WedgeDots, i], Element[WedgeDots, i + 1]], i, 1, NumberOfParts) → Wedges
  6. Element(Wedges, 1) → Wedge01
  7. Element(Wedges, 2) → Wedge02
  8. Element(Wedges, 3) → Wedge03
  9. Element(Wedges, 4) → Wedge04
  10. Element(Wedges, 5) → Wedge05
  11. Element(Wedges, 6) → Wedge06
  12. Element(Wedges, 7) → Wedge07
  13. Element(Wedges, 8) → Wedge08
  14. Element(Wedges, 9) → Wedge09
  15. Element(Wedges, 10) → Wedge10
  16. Element(Wedges, 11) → Wedge11
  17. Element(Wedges, 12) → Wedge12
  18. Element(Wedges, 13) → Wedge13
  19. Element(Wedges, 14) → Wedge14
  20. Element(Wedges, 15) → Wedge15
  21. Element(Wedges, 16) → Wedge16
  22. Element(Wedges, 17) → Wedge17
  23. Element(Wedges, 18) → Wedge18
  24. Element(Wedges, 19) → Wedge19
  25. Element(Wedges, 20) → Wedge20
  26. Segment(C, D) → g
  27. Segment(D, E) → h
  28. Segment(E, F) → i
  29. Segment(F, C) → j
  30. Sequence(C + ((StripWidth * i), 0), i, 0, NumberOfParts) → LowerDots
  31. Sequence(F + ((StripWidth * i), 0), i, 0, NumberOfParts) → UpperDots
  32. Sequence(Polygon[Element[LowerDots, i], Element[LowerDots, i + 1], Element[UpperDots, i + 1], Element[UpperDots, i]], i, 1, NumberOfParts) → VerticalStripsList
  33. Element(VerticalStripsList, 1) → Vertical01
  34. Element(VerticalStripsList, 2) → Vertical02
  35. Element(VerticalStripsList, 3) → Vertical03
  36. Element(VerticalStripsList, 4) → Vertical04
  37. Element(VerticalStripsList, 5) → Vertical05
  38. Element(VerticalStripsList, 6) → Vertical06
  39. Element(VerticalStripsList, 7) → Vertical07
  40. Element(VerticalStripsList, 8) → Vertical08
  41. Element(VerticalStripsList, 9) → Vertical09
  42. Element(VerticalStripsList, 10) → Vertical10
  43. Element(VerticalStripsList, 11) → Vertical11
  44. Element(VerticalStripsList, 12) → Vertical12
  45. Element(VerticalStripsList, 13) → Vertical13
  46. Element(VerticalStripsList, 14) → Vertical14
  47. Element(VerticalStripsList, 15) → Vertical15
  48. Element(VerticalStripsList, 16) → Vertical16
  49. Element(VerticalStripsList, 17) → Vertical17
  50. Element(VerticalStripsList, 18) → Vertical18
  51. Element(VerticalStripsList, 19) → Vertical19
  52. Element(VerticalStripsList, 20) → Vertical20
  53. Segment(G, H) → k
  54. Segment(H, I) → l
  55. Segment(I, J) → m
  56. Segment(J, G) → n
  57. Sequence(G + (0, (StripWidth * i)), i, 0, NumberOfParts) → LeftDots
  58. Sequence(H + (0, (StripWidth * i)), i, 0, NumberOfParts) → RightDots
  59. Sequence(Polygon[Element[LeftDots, i], Element[RightDots, i], Element[RightDots, i + 1], Element[LeftDots, i + 1]], i, 1, NumberOfParts) → HorizontalStripsList
  60. Element(HorizontalStripsList, 1) → Horizontal01
  61. Element(HorizontalStripsList, 2) → Horizontal02
  62. Element(HorizontalStripsList, 3) → Horizontal03
  63. Element(HorizontalStripsList, 4) → Horizontal04
  64. Element(HorizontalStripsList, 5) → Horizontal05
  65. Element(HorizontalStripsList, 6) → Horizontal06
  66. Element(HorizontalStripsList, 7) → Horizontal07
  67. Element(HorizontalStripsList, 8) → Horizontal08
  68. Element(HorizontalStripsList, 9) → Horizontal09
  69. Element(HorizontalStripsList, 10) → Horizontal10
  70. Element(HorizontalStripsList, 11) → Horizontal11
  71. Element(HorizontalStripsList, 12) → Horizontal12
  72. Element(HorizontalStripsList, 13) → Horizontal13
  73. Element(HorizontalStripsList, 14) → Horizontal14
  74. Element(HorizontalStripsList, 15) → Horizontal15
  75. Element(HorizontalStripsList, 16) → Horizontal16
  76. Element(HorizontalStripsList, 17) → Horizontal17
  77. Element(HorizontalStripsList, 18) → Horizontal18
  78. Element(HorizontalStripsList, 19) → Horizontal19
  79. Element(HorizontalStripsList, 20) → Horizontal20

AI Drawing Prompt Reference

Draw a circle to represent a whole, create perpendicular lines from the center to a horizontal line to divide the circle into equal parts, use sectors to represent each fractional part with different colors, and display rectangular strips to show the relationship between each part and the whole, controlled by a slider for the number of divisions to illustrate the geometric meaning of fractions.
The prompt above was compiled from the original drawing commands and is for reference only.