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Partitioning Composite Solids and Distributing Volumes (with Random Choice)

Partitioning Composite Solids and Distributing Volumes (with Random Choice)
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2024-09-05 16:09
Solid GeometryProbability & StatisticsTransformationGeometric ConstructionGraphing
In collections Rauminhalt zusammengesetzter Körper - Quader und Würfel
This example demonstrates how to split a composite solid (e.g., a body formed by combining orthogonal rectangular solids) into smaller geometric parts and use volume relationships to reason about how the total volume is distributed among the sub-solids. Key mathematical concepts include solid geometry, volume (Volumen), power-function ideas related to volume/measure scaling, and tangent-related geometric intuition (Tangente) to connect local geometric behavior with function understanding. It also incorporates probability via random variables (Zufallsvariablen or Zufallsgrößen) to randomize the selection of split options or practice steps. Construction and interaction highlights from the provided GeoGebra “construct summary”: Textfield for user inputs; Sum for aggregating sub-volume quantities; Shuffle and Element to randomly select from candidate elements/parameters; U and LaTeX for units and formula rendering; Segment and PolyLine to build the outlines/edges of parts; Translate and Dilate to move and scale parts consistently; If for conditional checking of answers; and listSteps plus counters such as attemptCountInputBox*, questionCount, and correctCount to manage step-by-step practice and validation. The workflow is supported by validate, showanswer, showsolution, and buttons like btnValidate/btnTryAgain/btnNew to guide learning and feedback. Suitable for late secondary school through early undergraduate levels, especially for teaching volume partitioning, measure scaling, and randomized practice/self-assessment.

GeoGebra Commands & Parameters

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Sum({attemptCountInputBox1, attemptCountInputBox2, attemptCountInputBox3, attemptCountInputBox4, attemptCountInputBox5}) → attemptCount
  4. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {7, 3, 10, 7, 4, 4, 6, 8, 5, 5, 2, 3, 3, 3, 4, 4, 9, 1, 0, 8, 6, 4, 8, 6, 7, 0, 7, 9, 1, 5, 8, 8, 3, 4, 7, 2, 0, 9, 4, 1, 9, 0, 10, 0, 6, 3, 6, 0, 0, 8, 10, 0, 4, 8, 5, 9, 6, 10, 2, 0, 3, 1, 1, 0, 2, 2, 4, 9, 5, 0, 7, 2, 3, 1, 7, 4, 0, 2, 2, 3, 2, 5, 9, 6, 5, 8, 6, 9, 0, 1, 10, 0, 5, 10, 4, 6, 5, 5, 10, 8}
  5. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  6. U(A, pointVec) → l1, l2, C, D, E, F, G, H, l0BG1, l4Kontur, l2Mantel, l4lines, l4linesManual, l5FG1, l5FG2, B
  7. LaTeX(step, true, true) → Text1
  8. Segment(pointOption1, F) → segmentOption1
  9. Segment(F, pointOption2) → segmentOption2
  10. Segment(E, pointOption3) → segmentOption3
  11. Segment(E, pointOption4) → segmentOption4
  12. Translate(C, pointVec) → C'
  13. Translate(pointOption4, pointVec) → pointOption4'
  14. Translate(F, pointVec) → F'
  15. Translate(G, pointVec) → G'
  16. Translate(H, pointVec) → H'
  17. If(option1, A, pointOption1) → pointObject11
  18. If(option1, pointOption2, F) → pointObject12
  19. Translate(D, pointVec) → D'
  20. Segment(pointOption4, pointOption4') → segmentOption41
  21. Translate(B, pointVec) → B'
  22. If(¬option4, pointOption4', B') → pointObject31
  23. If(¬option4, pointOption4, B) → pointObject32
  24. If(¬option4, E, pointOption3) → pointObject33
  25. If(option2 ∧ option4, 1, option1 ∧ option4, 2, option1 ∧ option3, 3, 4) → typ
  26. Segment(G', D') → segmentFilled1
  27. Segment(G, D) → segmentFilled2
  28. Segment(pointOption1, F) → segmentCutted1
  29. Segment(E, pointOption4) → segmentCutted2
  30. Segment(pointOption4, pointOption4') → segmentCutted3
  31. Segment(B', C') → f
  32. Segment(C', D') → g
  33. Segment(D', D) → h
  34. Segment(E', F') → i
  35. Segment(F', G') → j
  36. Segment(G', H') → k
  37. Segment(H', H) → l
  38. If(step ∈ {4, 5}, (-23.75, 32.5), (-23.75, 35)) → speechbubble12
  39. If(step ∈ {4, 5}, (0, 32.5), (3.75, 35)) → speechbubble13
  40. If(step ∈ {4, 5}, (0, 40.3), (3.75, 39.5)) → speechbubble14
  41. If(step ∈ {4, 5}, (-23.75, 40.3), (-23.75, 39.5)) → speechbubble15
  42. Textfield(input3) → InputBox3
  43. Textfield(input4) → InputBox4
  44. Textfield(input71) → InputBox71
  45. Textfield(input72) → InputBox72
  46. Textfield(input73) → InputBox73
  47. Textfield(input74) → InputBox74
  48. Textfield(input75) → InputBox75
  49. If((¬option1) ∧ (¬option2), input72 ≟ ((3 * 5) * 2), true) → correct72
  50. If((¬option3) ∧ (¬option4), input74 ≟ ((3 * 5) * 2), true) → correct74
  51. Dilate(Translate[l5FG2, (-10, 0)], step6Scalefactor, CenterOfDilation) → l3
  52. Dilate(Translate[listObject1, translationVector], step6Scalefactor, CenterOfDilation) → listObject1'
  53. Dilate(Translate[listObjectFilledLeftBottom, translationVector], step6Scalefactor, CenterOfDilation) → listObjectFilledLeftBottom'
  54. Dilate(Translate[listObjectFilledRightBottom, translationVector], step6Scalefactor, CenterOfDilation) → listObjectFilledRightBottom'
  55. Dilate(Segment[Translate[F, translationVector], Translate[pointOption2, translationVector]], step6Scalefactor, CenterOfDilation) → segmentOption2'
  56. Dilate(Segment[Translate[E, translationVector], Translate[pointOption3, translationVector]], step6Scalefactor, CenterOfDilation) → segmentOption3'
  57. Dilate(Segment[Translate[pointOption1, translationVector], Translate[F, translationVector]], step6Scalefactor, CenterOfDilation) → segmentOption1'
  58. Dilate(Translate[listObject3, translationVector], step6Scalefactor, CenterOfDilation) → listObject3'
  59. Dilate(Translate[listObject2, translationVector], step6Scalefactor, CenterOfDilation) → listObject2'
  60. Dilate(Translate[l0BG1, translationVector], step6Scalefactor, CenterOfDilation) → step6l0BG1'
  61. Dilate(Translate[l2Mantel, translationVector], step6Scalefactor, CenterOfDilation) → step6l2Mantel'
  62. Dilate(Translate[l4Kontur, translationVector], step6Scalefactor, CenterOfDilation) → step6l4Kontur'
  63. Dilate(Translate[l4linesManual, translationVector], step6Scalefactor, CenterOfDilation) → step6l4linesManual'
  64. Dilate(Translate[l5FG1, translationVector], step6Scalefactor, CenterOfDilation) → step6l5FG1'
  65. Dilate(Translate[l5FG2, translationVector], step6Scalefactor, CenterOfDilation) → step6l5FG2'
  66. Dilate(Segment[Translate[pointOption4, translationVector], Translate[pointOption4', translationVector]], step6Scalefactor, CenterOfDilation) → segmentOption41'
  67. Dilate(Translate[listObjectFilledRightBottom, translationVector], step6Scalefactor, CenterOfDilation) → listObjectFilledRightBottomBG'
  68. PolyLine(Dilate[B, step6Scalefactor, CenterOfDilation], Dilate[B', step6Scalefactor, CenterOfDilation], Dilate[A, step6Scalefactor, CenterOfDilation], Dilate[C', step6Scalefactor, CenterOfDilation], Dilate[D', step6Scalefactor, CenterOfDilation], Dilate[D, step6Scalefactor, CenterOfDilation], Dilate[E', step6Scalefactor, CenterOfDilation], Dilate[F', step6Scalefactor, CenterOfDilation], Dilate[G', step6Scalefactor, CenterOfDilation], Dilate[H', step6Scalefactor, CenterOfDilation], Dilate[H, step6Scalefactor, CenterOfDilation]) → m
  69. PolyLine(Translate[E, translationVector], Translate[pointOption4, translationVector], Translate[I', translationVector]) → n
  70. Dilate(PolyLine[Translate[E, translationVector], Translate[pointOption4, translationVector], Translate[I', translationVector]], step6Scalefactor, CenterOfDilation) → segmentOption4'
  71. Translate(cora, (7, 0)) → cora'
  72. Textfield(input31) → InputBox31
  73. Textfield(input32) → InputBox32
  74. Translate(elia, (30.434007263501044, -17.511741828561323)) → elia'
  75. Translate(Mirror[speechbubble2, x = -18], (0.5, -20)) → speechbubble3
  76. Textfield(input2a) → InputBox2a
  77. Textfield(input3a) → InputBox3a
  78. Textfield(input1a) → InputBox1a
  79. Textfield(input1b) → InputBox1b

AI Drawing Prompt Reference

Draw a composite solid formed by combining several orthogonal rectangular prisms, then split it into smaller sub-solids and show how the total volume is distributed among them. Include multiple input boxes for user-entered values, and use line segments and polylines to outline the faces of the solid. Apply translation and scaling to display the separated parts. Add a random selection mechanism to pick parameters from a set, and show step hints, answer validation buttons, and attempt counters. Arrange text fields, buttons, and counters to guide the user through the volume partitioning and distribution exercise.
The prompt above was compiled from the original drawing commands and is for reference only.