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相对频率与求和规则互动练习

相对频率与求和规则互动练习
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2024-06-06 18:30
函数概率统计滑块动画
所属专题 Arbeiten mit Baumdiagrammen
① 本范例是一个面向中学低年级的互动练习，通过随机生成数字列表，让学生计算相对频率并应用求和规则（即所有相对频率之和为1）。② 核心数学概念是概率统计中的相对频率、频率分布以及求和规则，同时涉及基本的计数和逻辑判断。③ 作图要点：从构造摘要看，使用了GeoGebra的Textfield（文本输入框）、Shuffle（随机打乱）、If（条件判断）、Join（合并）、Polygon（多边形）、Element（元素提取）、Append（追加）、Remove（移除）、Defined（定义检查）、Line（直线）、Segment（线段）、Mirror（镜像）、Text（文本）等命令，并设计了多个按钮（如验证、重试、新题）和输入框，用于交互式答题和反馈。④ 适合学段为5-6年级（约10-12岁），用于课堂练习或家庭作业，帮助学生直观理解相对频率的概念和求和规则，培养数据分析和逻辑推理能力。

GeoGebra 命令及参数

  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 绘图提示语参考

创建一个交互式概率学习界面，包含两个文本输入框用于用户回答问题。界面上方有验证、重试和新问题三个操作按钮。显示一个包含多种运动项目（如篮球、足球、游泳、网球、排球、徒步、舞蹈）的随机列表，每个运动项目旁边有对应的数值。画面中心绘制一棵概率树形图，从根节点分出多个分支，显示不同的概率路径。右侧有一个反馈区域，用矩形框显示正确答案或错误提示。底部有一个可拖动的滑块控件，用于调节某个概率参数。整个界面色彩鲜明，使用蓝色和绿色区分不同类型的元素，适合10-12岁学生使用。
以上提示语为根据原始绘图命令整理而来，仅供参考。