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Inkblot Task - Tree Diagram Counting Exercise

Inkblot Task - Tree Diagram Counting Exercise
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2024-06-06 18:29
PolygonSequenceProbability & StatisticsTransformationSlider Animation
In collections Arbeiten mit Baumdiagrammen
① This GeoGebra example presents an 'Inkblot Task' (Klecksaufgabe) that demonstrates how to use a tree diagram (Baumdiagramm) to systematically list all possible combinations, helping students visualize counting problems. ② The core mathematical concepts are the fundamental counting principle and tree diagram representation in probability and statistics, involving selecting and arranging elements from multiple sets. ③ Construction details: The applet uses GeoGebra commands such as Textfield, Shuffle, Element, Join, Polygon, Append, Remove, Defined, Line, Segment, Mirror, and Text, along with objects like color variables (Blue, Green, Orange, Red, Purple, Gray), interactive buttons (btnValidate, btnTryAgain, btnNew), input boxes (InputBox1, InputBox2), and dynamic text counters (textCountCorrect) to provide practice and feedback. ④ It is suitable for students in grades 5-6 or early middle school, serving as an exercise for classroom or homework, enhancing logical thinking and systematic enumeration skills, and can also be used by teachers for demonstration.

GeoGebra Commands & Parameters

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Shuffle(Sequence[i, i, 1, 8]) → ListExNum, {5, 1, 6, 3, 8, 4, 2, 7}
  4. Shuffle({1, 2, 3, 4, 5, 6}) → ListGesucht, {2, 5, 1, 3, 4, 6}
  5. Element(MatrixZahlen, exNum, gesucht) → sol
  6. Shuffle({1, 2}) → ListModus, {1, 2}
  7. Join({{1}, ListModus}) → ListeModusReal
  8. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  9. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {8, 9, 7, 9, 4, 1, 2, 5, 2, 9, 9, 4, 1, 0, 1, 0, 1, 9, 6, 4, 2, 0, 2, 1, 5, 10, 2, 7, 8, 10, 4, 2, 6, 4, 1, 8, 3, 5, 8, 6, 10, 1, 0, 8, 8, 3, 5, 8, 9, 1, 0, 9, 3, 3, 5, 9, 9, 7, 1, 8, 0, 6, 5, 2, 6, 10, 0, 8, 4, 0, 1, 9, 5, 4, 1, 2, 8, 3, 3, 1, 6, 2, 9, 4, 6, 9, 1, 8, 7, 8, 0, 6, 9, 5, 0, 2, 5, 0, 8, 3}
  10. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  11. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {10, 8, 1, 2, 2, 6, 2, 7, 5, 3, 3, 3, 1, 1, 8, 2, 9, 9, 1, 10, 0, 6, 3, 0, 9, 9, 2, 9, 3, 6, 1, 8, 7, 9, 2, 1, 0, 0, 1, 8, 2, 4, 10, 8, 1, 5, 0, 6, 10, 5, 2, 4, 3, 1, 6, 7, 0, 3, 9, 5, 5, 4, 5, 10, 6, 5, 7, 9, 4, 0, 6, 5, 2, 9, 0, 0, 3, 2, 5, 3, 4, 10, 7, 4, 9, 8, 8, 0, 2, 0, 10, 6, 2, 7, 9, 3, 5, 10, 8, 4}
  12. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  13. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  14. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  15. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  16. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  17. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  18. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  19. Defined(input1) → fixed
  20. Line(BaumZentrum, yAxis) → AchseSymm
  21. Segment(B, BaumAst1) → f
  22. Segment(D, BaumAst2) → g
  23. Mirror(D, Line[BaumAst1, yAxis]) → D'
  24. Mirror(BaumAst2, Line[BaumAst1, yAxis]) → E'
  25. Segment(D', E') → g'
  26. Mirror(Anchor6, Line[BaumAst1, yAxis]) → Anchor5
  27. Mirror(Anchor2, AchseSymm) → Anchor1
  28. Mirror(Anchor6, AchseSymm) → Anchor3
  29. Mirror(Anchor5, AchseSymm) → Anchor4
  30. Text(HelperText1, Anchor1, false, true, 0, 0) → Text7
  31. Text(HelperText2, Anchor2, false, true, 0, 0) → Text8
  32. Text(HelperText3, Anchor3, false, true, 0, 0) → Text9
  33. Text(HelperText4, Anchor4, false, true, 0, 0) → Text10
  34. Text(HelperText5, Anchor5, false, true, 0, 0) → Text11
  35. Text(HelperText6, Anchor6, false, true, 0, 0) → Text12
  36. Mirror(AnchorBT2, AchseSymm) → AnchorBT1
  37. Mirror(AnchorBT6, AchseSymm) → AnchorBT3
  38. Mirror(AnchorBT6, Line[BaumAst1, yAxis]) → AnchorBT5
  39. Mirror(AnchorBT5, AchseSymm) → AnchorBT4
  40. Text(HelperBT1, AnchorBT1, false, true, 0, 0) → Text1
  41. Text(HelperBT2, AnchorBT2, false, true, 0, 0) → Text3
  42. Text(HelperBT3, AnchorBT3, false, true, 0, 0) → Text4
  43. Text(HelperBT4, AnchorBT4, false, true, 0, 0) → Text5
  44. Text(HelperBT5, AnchorBT5, false, true, 0, 0) → Text6
  45. Text(HelperBT6, AnchorBT6, false, true, 0, 0) → Text13
  46. Text(Text16, AnchorInput + (0.7, 0.15), false, true, 0, 0) → Text17

AI Drawing Prompt Reference

Draw a tree diagram with two circular root nodes representing X and Y sets. Each set contains multiple elements connected by lines. The diagram also includes multiple rectangles representing correct and incorrect answers. The diagram has a vertical line at its center representing the Y-axis. The diagram has two circular branch points on its left and right sides representing the root nodes of the tree diagram. The diagram has two circular leaf nodes on its top and bottom sides representing the leaf nodes of the tree diagram. The diagram has two rectangles on its left and right sides representing correct and incorrect answers. The diagram has two rectangles on its top and bottom sides representing correct and incorrect answers. The diagram has a circular label at its center representing the intersection of X and Y sets.
The prompt above was compiled from the original drawing commands and is for reference only.