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Cross Table Puzzle: Reading Data from Contingency and Fourfold Tables

Cross Table Puzzle: Reading Data from Contingency and Fourfold Tables
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2024-08-19 21:35
FunctionSequenceProbability & Statistics
In collections Kreuztabellen
① This interactive math exercise demonstrates how to read and interpret data from cross tables (contingency tables) and fourfold tables. ② Core mathematical concepts include statistics and probability, specifically contingency tables, fourfold tables, data reading, and interpretation, with immediate feedback through randomized questions. ③ Construction highlights: using GeoGebra commands such as Shuffle, Element, If, Textfield, PolyLine, Sequence, and Text to build a random question system, including question text, validation buttons, feedback text boxes, hints, and correct count objects, enabling interactive practice through buttons and conditional logic. ④ Suitable for grades 7-8, this resource serves as classroom practice or self-study in statistics and probability, helping students develop skills in extracting and interpreting data from tables.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw an interactive-style 4×4 grid for a contingency/fourfold table exercise, with each cell forming a connected boxed matrix. Add bold category labels placed along the table areas, including “Obst essen”, “Kein Obst essen”, “häufig erkältet”, “nicht häufig erkältet”, and “Summe”. Place several numeric text entries inside specific cells centered in the cells, with one or more values visually emphasized depending on the current question. Include a single text input box for the learner’s typed answer and leave space for feedback/tip text so the figure supports immediate response.
The prompt above was compiled from the original drawing commands and is for reference only.