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交叉表谜题：从列联表与四格表中读取数据

交叉表谜题：从列联表与四格表中读取数据
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2024-08-19 21:35
函数数列概率统计
所属专题 Kreuztabellen
① 本范例是一个交互式数学练习，演示如何从交叉表（列联表）和四格表中读取数据并解释其含义。② 核心数学概念包括统计概率中的列联表、四格表、数据读取与解释，以及基于随机题目的即时反馈机制。③ 作图要点：使用 GeoGebra 的 Shuffle、Element、If、Textfield、PolyLine、Sequence、Text 等命令构建随机出题系统，包含题目文本、验证按钮、反馈文本框、提示信息、正确计数等对象，通过按钮和条件判断实现交互式练习。④ 适合初中7-8年级学生，用于统计概率模块的课堂练习或自主训练，帮助学生掌握从表格中提取信息并做出合理解释的能力。

GeoGebra 命令及参数

  1. Shuffle(1…numberOfQuestions) → randomQuestions, {9, 5, 2, 3, 6, 7, 8, 1, 4}
  2. Element(randomQuestions, Mod[questionCount - 1, Length[randomQuestions]] + 1) → randomQuestion
  3. If(randomQuestion ≟ 1, selected44, randomQuestion ≟ 6, selected23, randomQuestion ≟ 7, selected34, randomQuestion ≟ 8, selected43, selected32, randomQuestion ≟ 2, selected42, randomQuestion ≟ 3, selected24, randomQuestion ≟ 4, selected33, randomQuestion ≟ 5, selected22) → correct
  4. Textfield(input) → inputBox
  5. PolyLine(Vertex[zelle11(1), 1], Vertex[zelle11(1), 2], Vertex[zelle11(1), 3], Vertex[zelle11(1), 4], Vertex[zelle11(1), 1]) → PL11
  6. PolyLine(Vertex[zelle12(1), 1], Vertex[zelle12(1), 2], Vertex[zelle12(1), 3], Vertex[zelle12(1), 4], Vertex[zelle12(1), 1]) → PL12
  7. PolyLine(Vertex[zelle13(1), 1], Vertex[zelle13(1), 2], Vertex[zelle13(1), 3], Vertex[zelle13(1), 4], Vertex[zelle13(1), 1]) → PL13
  8. PolyLine(Vertex[zelle14(1), 1], Vertex[zelle14(1), 2], Vertex[zelle14(1), 3], Vertex[zelle14(1), 4], Vertex[zelle14(1), 1]) → PL14
  9. PolyLine(Vertex[zelle21(1), 1], Vertex[zelle21(1), 2], Vertex[zelle21(1), 3], Vertex[zelle21(1), 4], Vertex[zelle21(1), 1]) → PL21
  10. PolyLine(Vertex[zelle22(1), 1], Vertex[zelle22(1), 2], Vertex[zelle22(1), 3], Vertex[zelle22(1), 4], Vertex[zelle22(1), 1]) → PL22
  11. PolyLine(Vertex[zelle23(1), 1], Vertex[zelle23(1), 2], Vertex[zelle23(1), 3], Vertex[zelle23(1), 4], Vertex[zelle23(1), 1]) → PL23
  12. PolyLine(Vertex[zelle24(1), 1], Vertex[zelle24(1), 2], Vertex[zelle24(1), 3], Vertex[zelle24(1), 4], Vertex[zelle24(1), 1]) → PL24
  13. PolyLine(Vertex[zelle31(1), 1], Vertex[zelle31(1), 2], Vertex[zelle31(1), 3], Vertex[zelle31(1), 4], Vertex[zelle31(1), 1]) → PL31
  14. PolyLine(Vertex[zelle32(1), 1], Vertex[zelle32(1), 2], Vertex[zelle32(1), 3], Vertex[zelle32(1), 4], Vertex[zelle32(1), 1]) → PL32
  15. PolyLine(Vertex[zelle33(1), 1], Vertex[zelle33(1), 2], Vertex[zelle33(1), 3], Vertex[zelle33(1), 4], Vertex[zelle33(1), 1]) → PL33
  16. PolyLine(Vertex[zelle34(1), 1], Vertex[zelle34(1), 2], Vertex[zelle34(1), 3], Vertex[zelle34(1), 4], Vertex[zelle34(1), 1]) → PL34
  17. PolyLine(Vertex[zelle41(1), 1], Vertex[zelle41(1), 2], Vertex[zelle41(1), 3], Vertex[zelle41(1), 4], Vertex[zelle41(1), 1]) → PL41
  18. PolyLine(Vertex[zelle42(1), 1], Vertex[zelle42(1), 2], Vertex[zelle42(1), 3], Vertex[zelle42(1), 4], Vertex[zelle42(1), 1]) → PL42
  19. PolyLine(Vertex[zelle43(1), 1], Vertex[zelle43(1), 2], Vertex[zelle43(1), 3], Vertex[zelle43(1), 4], Vertex[zelle43(1), 1]) → PL43
  20. PolyLine(Vertex[zelle44(1), 1], Vertex[zelle44(1), 2], Vertex[zelle44(1), 3], Vertex[zelle44(1), 4], Vertex[zelle44(1), 1]) → PL44
  21. Sequence(Object[("txtQuestion0" * k)], k, 1, 9) → AllQuestions
  22. Text((((("\textsf{\textcolor{" * If[showsolution ∧ randomQuestion ≟ 5, "#006758", "#000000"]) * "}{") * If[showsolution ∧ randomQuestion ≟ 5, "\bold{", "{"]) * "5}}}"), If[layout ≟ -1, Midpoint[Vertex[zelle22(1), 1], Vertex[zelle22(1), 4]], layout ≟ 0, Midpoint[Vertex[zelle22(1), 1], Vertex[zelle22(1), 3]], Midpoint[Vertex[zelle22(1), 2], Vertex[zelle22(1), 3]]] + (0, 0.05), false, true, (-layout), 0) → txt22
  23. Text((((("\textsf{\textcolor{" * If[showsolution ∧ randomQuestion ≟ 6, "#006758", "#000000"]) * "}{") * If[showsolution ∧ randomQuestion ≟ 6, "\bold{", "{"]) * "5}"), If[layout ≟ -1, Midpoint[Vertex[zelle23(1), 1], Vertex[zelle23(1), 4]], layout ≟ 0, Midpoint[Vertex[zelle23(1), 1], Vertex[zelle23(1), 3]], Midpoint[Vertex[zelle23(1), 2], Vertex[zelle23(1), 3]]] + (0, 0.05), false, true, (-layout), 0) → txt23
  24. Text((((("\textsf{\textcolor{" * If[showsolution ∧ randomQuestion ≟ 3, "#006758", "#000000"]) * "}{") * If[showsolution ∧ randomQuestion ≟ 3, "\bold{", "{"]) * "10}"), If[layout ≟ -1, Midpoint[Vertex[zelle24(1), 1], Vertex[zelle24(1), 4]], layout ≟ 0, Midpoint[Vertex[zelle24(1), 1], Vertex[zelle24(1), 3]], Midpoint[Vertex[zelle24(1), 2], Vertex[zelle24(1), 3]]] + (0, 0.05), false, true, (-layout), 0) → txt24
  25. Text((((("\textsf{\textcolor{" * If[showsolution ∧ randomQuestion ≟ 9, "#006758", "#000000"]) * "}{") * If[showsolution ∧ randomQuestion ≟ 9, "\bold{", "{"]) * "7}"), If[layout ≟ -1, Midpoint[Vertex[zelle32(1), 1], Vertex[zelle32(1), 4]], layout ≟ 0, Midpoint[Vertex[zelle32(1), 1], Vertex[zelle32(1), 3]], Midpoint[Vertex[zelle32(1), 2], Vertex[zelle32(1), 3]]] + (0, 0.05), false, true, (-layout), 0) → txt32
  26. Text((((("\textsf{\textcolor{" * If[showsolution ∧ randomQuestion ≟ 4, "#006758", "#000000"]) * "}{") * If[showsolution ∧ randomQuestion ≟ 4, "\bold{", "{"]) * "3}"), If[layout ≟ -1, Midpoint[Vertex[zelle33(1), 1], Vertex[zelle33(1), 4]], layout ≟ 0, Midpoint[Vertex[zelle33(1), 1], Vertex[zelle33(1), 3]], Midpoint[Vertex[zelle33(1), 2], Vertex[zelle33(1), 3]]] + (0, 0.05), false, true, (-layout), 0) → txt33
  27. Text((((("\textsf{\textcolor{" * If[showsolution ∧ randomQuestion ≟ 7, "#006758", "#000000"]) * "}{") * If[showsolution ∧ randomQuestion ≟ 7, "\bold{", "{"]) * "10}"), If[layout ≟ -1, Midpoint[Vertex[zelle34(1), 1], Vertex[zelle34(1), 4]], layout ≟ 0, Midpoint[Vertex[zelle34(1), 1], Vertex[zelle34(1), 3]], Midpoint[Vertex[zelle34(1), 2], Vertex[zelle34(1), 3]]] + (0, 0.05), false, true, (-layout), 0) → txt34
  28. Text((((("\textsf{\textcolor{" * If[showsolution ∧ randomQuestion ≟ 2, "#006758", "#000000"]) * "}{") * If[showsolution ∧ randomQuestion ≟ 2, "\bold{", "{"]) * "12}"), If[layout ≟ -1, Midpoint[Vertex[zelle42(1), 1], Vertex[zelle42(1), 4]], layout ≟ 0, Midpoint[Vertex[zelle42(1), 1], Vertex[zelle42(1), 3]], Midpoint[Vertex[zelle42(1), 2], Vertex[zelle42(1), 3]]] + (0, 0.05), false, true, (-layout), 0) → txt42
  29. Text((((("\textsf{\textcolor{" * If[showsolution ∧ randomQuestion ≟ 8, "#006758", "#000000"]) * "}{") * If[showsolution ∧ randomQuestion ≟ 8, "\bold{", "{"]) * "8}"), If[layout ≟ -1, Midpoint[Vertex[zelle43(1), 1], Vertex[zelle43(1), 4]], layout ≟ 0, Midpoint[Vertex[zelle43(1), 1], Vertex[zelle43(1), 3]], Midpoint[Vertex[zelle43(1), 2], Vertex[zelle43(1), 3]]] + (0, 0.05), false, true, (-layout), 0) → txt43
  30. Text((((("\textsf{\textcolor{" * If[showsolution ∧ randomQuestion ≟ 1, "#006758", "#000000"]) * "}{") * If[showsolution ∧ randomQuestion ≟ 1, "\bold{", "{"]) * "20}"), If[layout ≟ -1, Midpoint[Vertex[zelle44(1), 1], Vertex[zelle44(1), 4]], layout ≟ 0, Midpoint[Vertex[zelle44(1), 1], Vertex[zelle44(1), 3]], Midpoint[Vertex[zelle44(1), 2], Vertex[zelle44(1), 3]]] + (0, 0.05), false, true, (-layout), 0) → txt44
  31. Text("\textsf{\bold{häufig erkältet}}", If[layout ≟ -1, Midpoint[Vertex[zelle12(1), 1], Vertex[zelle12(1), 4]], layout ≟ 0, Midpoint[Vertex[zelle12(1), 1], Vertex[zelle12(1), 3]], Midpoint[Vertex[zelle12(1), 2], Vertex[zelle12(1), 3]]] + (0, 0.05), false, true, (-layout), 0) → txt12
  32. Text("\textsf{\bold{nicht häufig erkältet}}", If[layout ≟ -1, Midpoint[Vertex[zelle13(1), 1], Vertex[zelle13(1), 4]], layout ≟ 0, Midpoint[Vertex[zelle13(1), 1], Vertex[zelle13(1), 3]], Midpoint[Vertex[zelle13(1), 2], Vertex[zelle13(1), 3]]] + (0, 0.05), false, true, (-layout), 0) → txt13
  33. Text("\textsf{\bold{Summe}}", If[layout ≟ -1, Midpoint[Vertex[zelle14(1), 1], Vertex[zelle14(1), 4]], layout ≟ 0, Midpoint[Vertex[zelle14(1), 1], Vertex[zelle14(1), 3]], Midpoint[Vertex[zelle14(1), 2], Vertex[zelle14(1), 3]]] + (0, 0.05), false, true, (-layout), 0) → txt14
  34. Text("\textsf{\bold{Obst essen}}", If[layout ≟ -1, Midpoint[Vertex[zelle21(1), 1], Vertex[zelle21(1), 4]], layout ≟ 0, Midpoint[Vertex[zelle21(1), 1], Vertex[zelle21(1), 3]], Midpoint[Vertex[zelle21(1), 2], Vertex[zelle21(1), 3]]] + (0, 0.05), false, true, (-layout), 0) → txt21
  35. Text("\textsf{\bold{Kein Obst essen}}", If[layout ≟ -1, Midpoint[Vertex[zelle31(1), 1], Vertex[zelle31(1), 4]], layout ≟ 0, Midpoint[Vertex[zelle31(1), 1], Vertex[zelle31(1), 3]], Midpoint[Vertex[zelle31(1), 2], Vertex[zelle31(1), 3]]] + (0, 0.05), false, true, (-layout), 0) → txt31
  36. Text("\textsf{\bold{Summe}}", If[layout ≟ -1, Midpoint[Vertex[zelle41(1), 1], Vertex[zelle41(1), 4]], layout ≟ 0, Midpoint[Vertex[zelle41(1), 1], Vertex[zelle41(1), 3]], Midpoint[Vertex[zelle41(1), 2], Vertex[zelle41(1), 3]]] + (0, 0.05), false, true, (-layout), 0) → txt41

AI 绘图提示语参考

绘制一个用于四格表/列联表练习的统计图：画出一个以网格方式排列的 4×4 方格区域，并将每个格子用矩形边框连成整体；在表的右侧边界放置四段加粗的单词标签作为行/列含义（可见“Obst essen”“Kein Obst essen”“häufig erkältet”“nicht häufig erkältet”“Summe”）；同时在若干指定单元格中心位置写入表内数字文本，数字会随题目高亮变化。最后在图中准备一个可输入的文本框，用来填写对当前题目的读取结果，并预留“正确/反馈/提示”文字区域以支持互动。
以上提示语为根据原始绘图命令整理而来，仅供参考。