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Relative Frequencies - Sum Rule Interactive Exercise

Relative Frequencies - Sum Rule Interactive Exercise
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2024-06-06 18:30
FunctionProbability & StatisticsSlider Animation
In collections Arbeiten mit Baumdiagrammen
① This interactive GeoGebra example demonstrates the concept of relative frequencies and the sum rule (that all relative frequencies add up to 1) through a randomized number-list exercise. ② Core mathematical concepts include relative frequency, frequency distribution, and the sum rule in probability and statistics, along with basic counting and logical reasoning. ③ Construction highlights: based on the construction summary, the applet uses GeoGebra commands such as Textfield, Shuffle, If, Join, Polygon, Element, Append, Remove, Defined, Line, Segment, Mirror, and Text, and includes multiple buttons (validate, try again, new problem) and input boxes for interactive answering and feedback. ④ It is suitable for grades 5-6 (ages 10-12) as a classroom activity or homework, helping students intuitively grasp relative frequency and the sum rule while developing data analysis and logical thinking skills.

GeoGebra Commands & Parameters

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Shuffle(Sequence[i, i, 1, 8]) → ListExNum, {2, 4, 1, 6, 8, 7, 3, 5}
  4. Shuffle({2, 3, 4, 5, 6}) → ListGesucht, {2, 3, 6, 4, 5}
  5. If(questionCount < 3, questionCount, 3) → metaorder
  6. Shuffle(3…5) → ListGesuchtStart, {4, 3, 5}
  7. Join({{ListGesuchtStart(1)}, ListGesucht}) → ListGesuchtReal
  8. If(questionCount ≟ 0, 0, 1) → metahalper
  9. Shuffle(Sequence[i, i, 1, 8]) → ListRandomNumbers1, {5, 8, 7, 6, 2, 4, 3, 1}
  10. Shuffle(Sequence[i, i, 1, 10 - (ListRandomNumbers1(1) + 1)]) → ListRandomNumbers2, {1, 3, 4, 2}
  11. Shuffle({"Basketball", "Tanzen", "Volleyball", "Schwimmen", "Wandern", "Fußball", "Tennis"}) → ListSportarten, {"Tanzen", "Fußball", "Wandern", "Basketball", "Schwimmen", "Tennis", "Volleyball"}
  12. Shuffle(Sequence[ListSportarten(i), i, 1, 2]) → ListeGesucht1, {"Fußball", "Tanzen"}
  13. Shuffle(Sequence[ListSportarten(i), i, 3, 4]) → ListeGesucht2, {"Basketball", "Wandern"}
  14. If(SportartGesucht1 ≟ ListSportarten(1), 1, 2) → ebene1gesucht
  15. If(SportartGesucht2 ≟ ListSportarten(3), 1, 2) → ebene2gesucht
  16. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  17. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {2, 3, 8, 9, 3, 1, 10, 2, 9, 0, 0, 6, 10, 7, 4, 2, 9, 4, 3, 2, 3, 3, 2, 6, 2, 9, 6, 7, 10, 9, 8, 10, 5, 8, 5, 6, 2, 8, 8, 3, 8, 4, 3, 1, 3, 0, 8, 8, 7, 9, 2, 10, 4, 10, 0, 7, 9, 5, 6, 6, 8, 8, 10, 9, 8, 8, 4, 8, 2, 3, 0, 9, 6, 7, 0, 8, 8, 6, 4, 6, 9, 9, 5, 9, 2, 3, 5, 10, 2, 1, 10, 8, 4, 5, 8, 2, 9, 6, 3, 3}
  18. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  19. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {0, 0, 1, 10, 1, 3, 6, 0, 4, 7, 2, 7, 0, 1, 4, 1, 1, 6, 8, 9, 9, 7, 10, 5, 10, 6, 5, 9, 6, 4, 10, 9, 4, 9, 0, 8, 0, 9, 2, 5, 8, 1, 6, 7, 8, 8, 0, 8, 10, 6, 8, 8, 9, 10, 3, 6, 0, 0, 4, 0, 10, 3, 4, 0, 9, 4, 0, 7, 8, 0, 10, 7, 4, 9, 8, 8, 4, 4, 8, 8, 6, 8, 0, 4, 9, 4, 4, 3, 3, 0, 9, 2, 5, 3, 6, 5, 7, 2, 8, 9}
  20. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  21. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  22. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  23. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  24. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  25. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  26. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  27. Defined(input1) → fixed
  28. Line(BaumZentrum, yAxis) → AchseSymm
  29. Segment(B, BaumAst1) → level3
  30. Segment(D, BaumAst2) → level33
  31. Mirror(D, Line[AnchorBT2, yAxis]) → D'
  32. Mirror(BaumAst2, Line[BaumAst1, yAxis]) → E'
  33. Shuffle({1, 2}) → ListModus, {1, 2}
  34. Mirror(Anchor12, Line[BaumAst1, yAxis]) → Anchor10
  35. Mirror(Anchor3, AchseSymm) → Anchor1
  36. Mirror(Anchor12, AchseSymm) → Anchor4
  37. Mirror(Anchor10, AchseSymm) → Anchor6
  38. Text(HelperText1, Anchor1, false, true, 0, 0) → NormTxt1
  39. Mirror(AnchorBT3, AchseSymm) → AnchorBT1
  40. Mirror(AnchorBT12, AchseSymm) → AnchorBT4
  41. Mirror(AnchorBT12, Line[BaumAst1, yAxis]) → AnchorBT10
  42. Mirror(AnchorBT10, AchseSymm) → AnchorBT6
  43. Segment(Mirror[B, AchseSymm], Mirror[BaumAst1, AchseSymm]) → level1
  44. Segment(Mirror[D, AchseSymm], Mirror[BaumAst2, AchseSymm]) → level11
  45. If(gesucht ≟ 2, 1, gesucht ≟ 3, 2, gesucht ≟ 4, 3, gesucht ≟ 5, 2, gesucht ≟ 6, 1) → anzahlpfade
  46. Segment(BaumZentrum, E) → level2
  47. Mirror(F, AchseSymm) → F'
  48. Segment(F, F + Vector[D, BaumAst2]) → level23
  49. Mirror(level23, AchseSymm) → level21
  50. Segment(G, J) → level22
  51. Mirror(I, AchseSymm) → I'
  52. Mirror(K, AchseSymm) → K'
  53. Mirror(AnchorBT9, AchseSymm) → AnchorBT7
  54. Mirror(AnchorBT11, AchseSymm) → AnchorBT5
  55. Mirror(Anchor9, AchseSymm) → Anchor7
  56. Text(HelperText3, Anchor3, false, true, 0, 0) → NormTxt3
  57. Text(HelperText2, Anchor2, false, true, 0, 0) → NormTxt2
  58. Text(HelperText1, Anchor4, false, true, 0, 0) → NormTxt11
  59. Text(HelperText3, Anchor6, false, true, 0, 0) → NormTxt13
  60. Text(HelperText2, Anchor5, false, true, 0, 0) → NormTxt12
  61. Text(HelperText2, Anchor8, false, true, 0, 0) → NormTxt22
  62. Text(HelperText2, Anchor11, false, true, 0, 0) → NormTxt32
  63. Text(HelperText1, Anchor7, false, true, 0, 0) → NormTxt21
  64. Text(HelperText1, Anchor10, false, true, 0, 0) → NormTxt31
  65. Text(HelperText3, Anchor9, false, true, 0, 0) → NormTxt23
  66. Text(HelperText3, Anchor12, false, true, 0, 0) → NormTxt33
  67. Segment(D, K) → level32
  68. Segment(D', K') → level12
  69. Segment(Mirror[D', AchseSymm], E') → level31
  70. Segment(D', Mirror[E', AchseSymm]) → level13
  71. Text(Text3Punkt, AnchorBT3 + (0, -0.2), false, true, 0, 0) → Txt3Punkt1
  72. Text(Text2Punkt, AnchorBT2 + (0, -0.2), false, true, 0, 0) → Txt2Punkt1
  73. Text(Text1Punkt, AnchorBT1 + (0, -0.2), false, true, 0, 0) → Txt1Punkt1
  74. Text(Text1Punkt, AnchorBT4 + (0, -0.2), false, true, 0, 0) → Txt1Punkt2
  75. Text(Text2Punkt, AnchorBT5 + (0, -0.2), false, true, 0, 0) → Txt2Punkt2
  76. Text(Text3Punkt, AnchorBT6 + (0, -0.2), false, true, 0, 0) → Txt3Punkt2
  77. Text(Text3Punkt, AnchorBT12 + (0, -0.2), false, true, 0, 0) → Txt3Punkt4
  78. Text(Text2Punkt, AnchorBT11 + (0, -0.2), false, true, 0, 0) → Txt2Punkt4
  79. Text(Text1Punkt, AnchorBT10 + (0, -0.2), false, true, 0, 0) → Txt1Punkt4
  80. Text(Text2Punkt, AnchorBT8 + (0, -0.2), false, true, 0, 0) → Txt2Punkt3
  81. Text(Text1Punkt, AnchorBT7 + (0, -0.2), false, true, 0, 0) → Txt1Punkt3
  82. Text(Text3Punkt, AnchorBT9 + (0, -0.2), false, true, 0, 0) → Txt3Punkt3
  83. Text(HelperSolTxt1, Anchor1, false, true, 0, 0) → SolTxt1
  84. Text(HelperSolTxt2, Anchor2, false, true, 0, 0) → SolTxt2
  85. Text(HelperSolTxt3, Anchor3, false, true, 0, 0) → SolTxt3
  86. Text(HelperSolTxt11, Anchor4, false, true, 0, 0) → SolTxt11
  87. Text(HelperSolTxt13, Anchor6, false, true, 0, 0) → SolTxt13
  88. Text(HelperSolTxt12, Anchor5, false, true, 0, 0) → SolTxt12
  89. Text(HelperSolTxt21, Anchor7, false, true, 0, 0) → SolTxt21
  90. Text(HelperSolTxt22, Anchor8, false, true, 0, 0) → SolTxt22
  91. Text(HelperSolTxt23, Anchor9, false, true, 0, 0) → SolTxt23
  92. Text(HelperSolTxt31, Anchor10, false, true, 0, 0) → SolTxt31
  93. Text(HelperSolTxt32, Anchor11, false, true, 0, 0) → SolTxt32
  94. Text(HelperSolTxt33, Anchor12, false, true, 0, 0) → SolTxt33

AI Drawing Prompt Reference

Create an interactive probability learning interface with two text input boxes for user answers. At the top include three operation buttons: Validate, Try Again, and New Problem. Display a randomized list of sports items such as basketball, soccer, swimming, tennis, volleyball, hiking, and dancing, each with corresponding numerical values next to it. In the center of the画面, draw a probability tree diagram branching from a root node showing different probability paths. On the right side, there is a feedback area with rectangular boxes showing correct answers or error messages. At the bottom, include a draggable slider control to adjust a probability parameter. The interface uses bright colors with blue and green to distinguish different types of elements, suitable for students aged 10-12.
The prompt above was compiled from the original drawing commands and is for reference only.