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The Big Wheel Challenge: Probability Intuition

The Big Wheel Challenge: Probability Intuition
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2024-06-19 17:27
CirclePolygonSequenceProbability & StatisticsSlider Animation
In collections Wahrscheinlichkeitsrechnung - Einführung
This interactive GeoGebra activity, titled 'The Big Wheel Challenge', simulates a spinning wheel game to help students develop an intuitive understanding of probability. It focuses on core concepts such as random events, equally likely outcomes, and quantifying uncertainty using probability. The construction uses commands like RandomElement, If, Element, Remove, Join, Point, IndexOf, Textfield, Circle, Sequence, CircleSector, Polygon, PolyLine, and Text to generate random questions, build the wheel with sectors, and manage interactive elements. Suitable for grades 7-8, it can be shared via Google Classroom or GeoGebra Lesson for classroom practice, emphasizing the use of intuitive probability to assess likelihood.

GeoGebra Commands & Parameters

  1. RandomElement(1…3) → Cat1
  2. If(Cat1 ≠ 1, 1, RandomElement[{2, 3}]) → Cat2
  3. Element(Remove[1…3, {Cat1, Cat2}], 1) → Cat3
  4. Remove(1…7, Join[{Set1, Set2}]) → Set3
  5. If(shuffled, Join[{Set1, Set2, Set3}], 1…numberOfQuestions) → randomQuestions
  6. Element(randomQuestions, Mod[questionCount - 1, Length[randomQuestions]] + 1) → randomQuestion
  7. If(questionCount ≟ 0 ∨ showGoal, einteilung0, EinteilungsListe(randomQuestion)) → einteilung
  8. If(randomQuestion ≟ 5, 90, 60) → index
  9. Join({Sequence[MP + ((2 * radius / 3) * (cos(((-index))° - (360° * (Sum[einteilung, k] - einteilung(k) / 2) / Sum[einteilung])), sin(((-index))° - (360° * (Sum[einteilung, k] - einteilung(k) / 2) / Sum[einteilung])))), k, 1, Length[einteilung]] + (-0.5, 0.48), Reverse[Sequence[StartStar + (k * (MP + ((-radius) - 1, 0) - StartStar)), k, 0, 1, 0.05]]}) → PosStarList
  10. Point(PosStarList) → PosStar
  11. IndexOf(PosStar, PosStarList) → StarIndex
  12. If(randomQuestion ≟ 1, correct1, randomQuestion ≟ 6, correct6, randomQuestion ≟ 7, correct7, false, randomQuestion ≟ 2, correct2, randomQuestion ≟ 3, correct3, randomQuestion ≟ 4, correct4, randomQuestion ≟ 5, correct5) → correct
  13. Textfield(input) → inputBox
  14. Circle(MP, radius) → glücksrad1
  15. Circle(MP, radius + 0.3) → glücksrad2
  16. Sequence(MP + (radius * (cos(360° - k°), sin(360° - k°))), k, 1, 360) → PGRList
  17. Sequence(MP + (radius * (cos(((-index))° - (360° * Sum[einteilung, k] / Sum[einteilung])), sin(((-index))° - (360° * Sum[einteilung, k] / Sum[einteilung])))), k, 1, Length[einteilung]) → PosGRList
  18. Sequence(Segment[PosGRList(k), MP], k, 1, Length[PosGRList]) → SegList
  19. CircleSector(MP, PosGRList(1), PosGRList(Length[PosGRList])) → sek1
  20. CircleSector(MP, PosGRList(2), PosGRList(1)) → sek2
  21. CircleSector(MP, PosGRList(3), PosGRList(2)) → sek3
  22. CircleSector(MP, PosGRList(4), PosGRList(3)) → sek4
  23. CircleSector(MP, PosGRList(5), PosGRList(4)) → sek5
  24. CircleSector(MP, PosGRList(6), PosGRList(5)) → sek6
  25. CircleSector(MP, PosGRList(7), PosGRList(6)) → sek7
  26. Polygon(PosStar, PosStar + (1, 0), PosStar + (1, -0.96), PosStar + (0, -0.96)) → polyStar, posstar, f, g, h
  27. PolyLine({PosSB, Corner[txt001, 1] + (0.25 * (Corner[txt001, 4] - Corner[txt001, 1])), Corner[txt001, 1], Corner[txt001, 2] + (0.2, 0), Corner[txt001, 3] + (0.2, 0.15), Corner[txt001, 4] + (0, 0.15), Corner[txt001, 1] + (0.25 * (Corner[txt001, 4] - Corner[txt001, 1])) + (0, 0.75), PosSB}) → sb00
  28. Circle(MP1, radius2) → gr11
  29. Circle(MP1, (radius2 * 1.13)) → gr12
  30. Circle(MP2, radius2) → gr21
  31. Circle(MP3, radius2) → gr31
  32. Circle(MP4, radius2) → gr41
  33. Circle(MP2, (radius2 * 1.13)) → gr22
  34. Circle(MP3, (radius2 * 1.13)) → gr32
  35. Circle(MP4, (radius2 * 1.13)) → gr42
  36. Sequence(MP1 + (radius2 * (cos((-(indexGR1°)) - (360° * Sum[einteilungGR1, k] / Sum[einteilungGR1])), sin((-(indexGR1°)) - (360° * Sum[einteilungGR1, k] / Sum[einteilungGR1])))), k, 1, Length[einteilungGR1]) → PosGR1List
  37. Sequence(Segment[PosGR1List(k), MP1], k, 1, Length[PosGR1List]) → SegList1
  38. If(randomQuestion ≟ 1 ∨ randomQuestion ≟ 6, {30, 20, 5, 45}, {25, 12.5, 12.5, 25, 25}) → einteilungGR2
  39. Sequence(MP2 + (radius2 * (cos((-(indexGR2°)) - (360° * Sum[einteilungGR2, k] / Sum[einteilungGR2])), sin((-(indexGR2°)) - (360° * Sum[einteilungGR2, k] / Sum[einteilungGR2])))), k, 1, Length[einteilungGR2]) → PosGR2List
  40. Sequence(Segment[PosGR2List(k), MP2], k, 1, Length[PosGR2List]) → SegList2
  41. If(randomQuestion ≟ 1 ∨ randomQuestion ≟ 6, {25, 25, 25, 12.5, 12.5}, {1, 1, 1, 1}) → einteilungGR3
  42. If(randomQuestion ≟ 3, 25, 60) → indexGR4
  43. If(randomQuestion ≟ 1 ∨ randomQuestion ≟ 6, {25, 25, 50}, {1 / 3, 1 / 4, 5 / 36, 5 / 36, 5 / 36}) → einteilungGR4
  44. Sequence(MP3 + (radius2 * (cos(((-indexGR3))° - (360° * Sum[einteilungGR3, k] / Sum[einteilungGR3])), sin(((-indexGR3))° - (360° * Sum[einteilungGR3, k] / Sum[einteilungGR3])))), k, 1, Length[einteilungGR3]) → PosGR3List
  45. Sequence(MP4 + (radius2 * (cos(((-indexGR4))° - (360° * Sum[einteilungGR4, k] / Sum[einteilungGR4])), sin(((-indexGR4))° - (360° * Sum[einteilungGR4, k] / Sum[einteilungGR4])))), k, 1, Length[einteilungGR4]) → PosGR4List
  46. Sequence(Segment[PosGR3List(k), MP3], k, 1, Length[PosGR3List]) → SegList3
  47. Sequence(Segment[PosGR4List(k), MP4], k, 1, Length[PosGR4List]) → SegList4
  48. CircleSector(MP1, PosGR1List(1), PosGR1List(Length[PosGR1List])) → sek11
  49. CircleSector(MP1, PosGR1List(2), PosGR1List(1)) → sek12
  50. CircleSector(MP1, PosGR1List(3), PosGR1List(2)) → sek13
  51. CircleSector(MP1, PosGR1List(4), PosGR1List(3)) → sek14
  52. CircleSector(MP3, PosGR3List(1), PosGR3List(Length[PosGR3List])) → sek32
  53. CircleSector(MP3, PosGR3List(2), PosGR3List(1)) → sek31
  54. CircleSector(MP3, PosGR3List(3), PosGR3List(2)) → sek33
  55. CircleSector(MP3, PosGR3List(4), PosGR3List(3)) → sek34
  56. CircleSector(MP3, PosGR3List(5), PosGR3List(4)) → sek35
  57. CircleSector(MP2, PosGR2List(1), PosGR2List(Length[PosGR2List])) → sek21
  58. CircleSector(MP2, PosGR2List(2), PosGR2List(1)) → sek22
  59. CircleSector(MP2, PosGR2List(3), PosGR2List(2)) → sek23
  60. CircleSector(MP2, PosGR2List(4), PosGR2List(3)) → sek24
  61. CircleSector(MP2, PosGR2List(5), PosGR2List(4)) → sek25
  62. CircleSector(MP4, PosGR4List(1), PosGR4List(Length[PosGR4List])) → sek41
  63. CircleSector(MP4, PosGR4List(2), PosGR4List(1)) → sek42
  64. CircleSector(MP4, PosGR4List(3), PosGR4List(2)) → sek43
  65. CircleSector(MP4, PosGR4List(4), PosGR4List(3)) → sek44
  66. CircleSector(MP4, PosGR4List(5), PosGR4List(4)) → sek45
  67. Text("\textsf{✘}", MP1 + (0, (-radius2) - GRHöhe2 - 1.25), false, true, 0, 0) → FB11
  68. Text(If[randomQuestion ≟ 3, "\textsf{✓}", "\textsf{✘}"], MP2 + (0, (-radius2) - GRHöhe2 - 1.25), false, true, 0, 0) → FB12
  69. Text(If[randomQuestion ≟ 6, "\textsf{✓}", "\textsf{✘}"], MP3 + (0, (-radius2) - GRHöhe2 - 1.25), false, true, 0, 0) → FB13
  70. Text(If[randomQuestion ≟ 1, "\textsf{✓}", "\textsf{✘}"], MP4 + (0, (-radius2) - GRHöhe2 - 1.25), false, true, 0, 0) → FB14
  71. Text("\textsf{✘}", Midpoint[Corner[txtOptionSC2, 1], Corner[txtOptionSC2, 4]] + (8, 0.15), false, true, 0, 0) → FB22
  72. Text(If[randomQuestion ≟ 2, "\textsf{✓}", "\textsf{✘}"], Midpoint[Corner[txtOptionSC1, 1], Corner[txtOptionSC1, 4]] + (8, 0.15), false, true, 0, 0) → FB21
  73. Text(If[randomQuestion ≟ 7, "\textsf{✓}", "\textsf{✘}"], Midpoint[Corner[txtOptionSC3, 1], Corner[txtOptionSC3, 4]] + (8, 0.15), false, true, 0, 0) → FB23
  74. If(randomQuestion ∈ {1, 3, 6}, optionGR1 ∨ optionGR2 ∨ optionGR3 ∨ optionGR4, randomQuestion ∈ {2, 7}, optionSC1 ∨ optionSC2 ∨ optionSC3, randomQuestion ≟ 4, StarIndex ∈ (1…Length[einteilung4]), randomQuestion ≟ 5, StarIndex ∈ (1…Length[einteilung5]), true) → clickableBtnValidate
  75. PolyLine({PosSB, Corner[txtGoal, 1] + (0.25 * (Corner[txtGoal, 4] - Corner[txtGoal, 1])), Corner[txtGoal, 1], Corner[txtGoal, 2] + (0.2, 0), Corner[txtGoal, 3] + (0.2, 0.15), Corner[txtGoal, 4] + (0, 0.15), Corner[txtGoal, 1] + (0.25 * (Corner[txtGoal, 4] - Corner[txtGoal, 1])) + (0, 0.75), PosSB}) → sbGoal
  76. Text(If[correct, "\textsf{✓ Richtig}", "\textsf{✘ Falsch}"], MP4 + (radius2, (-radius2) - GRHöhe2 - 2.25) + (-6.15, 0), false, true, 0, 0) → txtFeedback136
  77. Text(If[correct, "\textsf{✓ Richtig}", "\textsf{✘ Falsch}"], (0.2, 0.15) + (1, 0), false, true, 1, 0) → txtFeedback27

AI Drawing Prompt Reference

Draw a central “big wheel” spinner: place a main circle with a circle center, and add an additional slightly offset concentric circle to show the wheel boundary. Subdivide the wheel by defining several points on the circumference and connect consecutive boundary rays from the center to form multiple wedge (sector) regions arranged around the full circle; render these sectors with clear outlines so each slice is visually distinct. Around the wheel, add a fixed arrow/indicator-like polyline composed of connected segments with a few bend points, positioned relative to the same center. Include a text input box style label near the wheel and add small text annotations to mark the different options corresponding to the wheel sectors.
The prompt above was compiled from the original drawing commands and is for reference only.