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几何体分类练习

几何体分类练习
几何画板及绘图内容加载中，请稍等……
2025-07-30 16:15
所属专题 Wiederholung: Quader und Würfel
本范例通过几何体分类练习，帮助学生理解立方体等几何体的概念。涉及的核心数学概念包括几何体的分类和基本性质。使用了GeoGebra命令如Polygon, Max, If, Textfield等进行图形构造。适合7-8年级学生进行练习，有助于提高他们解决与立方体相关问题的能力。

GeoGebra 命令及参数

  1. Polygon(allowedRect4, allowedRect3, allowedRect2, allowedRect1) → allowedRect, a_1, b, c, d
  2. Max(widthsOptionsR) → widthR
  3. Max(heightsOptionsR) → heightR
  4. Max(heightR, Max[heightsOptionsL]) → heightL
  5. Max(widthsOptionsL) → widthL
  6. If(isShuffleOptionsLechts, Shuffle[1…numOptionsR], 1…numOptionsR) → indizesOptionsRechts
  7. If(isShuffleOptionsLinks, Shuffle[1…numOptionsL], 1…numOptionsL) → indizesOptionsLinks
  8. Textfield(input1) → InputBox1
  9. Textfield(input2) → InputBox2
  10. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  11. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {3, 4, 10, 6, 8, 1, 3, 2, 5, 6, 9, 6, 3, 10, 9, 0, 1, 1, 10, 8, 2, 1, 6, 2, 5, 9, 0, 5, 8, 1, 5, 4, 4, 9, 1, 10, 10, 6, 0, 4, 3, 9, 4, 7, 3, 1, 5, 4, 4, 1, 8, 2, 6, 3, 8, 7, 6, 4, 5, 6, 10, 8, 0, 0, 6, 10, 4, 4, 10, 7, 0, 2, 3, 4, 7, 7, 10, 4, 10, 2, 9, 1, 4, 1, 3, 7, 2, 1, 4, 5, 0, 0, 9, 7, 10, 1, 10, 1, 3, 2}
  12. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  13. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {8, 8, 5, 7, 10, 4, 0, 6, 10, 10, 1, 2, 8, 9, 10, 1, 7, 10, 9, 3, 9, 3, 5, 6, 4, 10, 9, 3, 6, 6, 1, 0, 7, 9, 8, 1, 10, 5, 6, 6, 2, 7, 8, 7, 5, 10, 1, 3, 7, 8, 10, 1, 6, 5, 9, 5, 4, 0, 0, 9, 2, 2, 9, 6, 6, 1, 0, 0, 4, 0, 1, 9, 8, 8, 1, 8, 9, 9, 3, 7, 4, 5, 4, 8, 7, 7, 1, 1, 2, 4, 0, 4, 1, 4, 5, 6, 5, 2, 2, 7}
  14. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  15. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  16. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  17. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  18. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  19. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  20. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  21. Sequence(1) → positionsOptionsRechts
  22. Sequence(Element[optionsRAll, indizesOptionsRechts(i)], i, 1, numOptionsR) → optionsRActual
  23. Length(optionsRActual) → a
  24. Sequence(Element[optionsLAll, indizesOptionsLinks(i)], i, 1, numOptionsL) → optionsLActual
  25. Sequence(allOptionsL(indizesOptionsLinks(i)), i, 1, numOptionsL) → optionsL
  26. Sequence(allOptionsR(indizesOptionsLinks(i)), i, 1, numOptionsL) → optionsR
  27. Polygon((-10, -2), (10, -2), (10, 10), (-10, 10)) → q1, q_1, r_1, s_1, t_1
  28. Polygon(E, F, G, H) → q2, e_1, f_2, g_2, h_2
  29. Polygon(I, J, K, L) → q3, i_2, j_2, k_1, l_1
  30. SpeechBubbleRight(O, 5, 2) → poly1
  31. Text(optionsLActual(6), CenterOptionL6, true, true, 0, 0) → opL6
  32. Text(optionsLActual(7), CenterOptionL7, true, true, 0, 0) → opL7
  33. Text(optionsLActual(8), CenterOptionL8, true, true, 0, 0) → opL8
  34. PointIn(allowedRect) → CenterOptionR8
  35. Text(optionsRActual(8), CenterOptionR8, true, true, 0, 0) → opR8
  36. Polygon(CenterOptionR8, CenterOptionR8 - (widthR / 2, heightR / 2), CenterOptionR8 + (widthR / 2, ((-heightR)) / 2), CenterOptionR8 + (widthR / 2, heightR / 2), CenterOptionR8 - (widthR / 2, ((-heightR)) / 2), CenterOptionR8 - (widthR / 2, heightR / 2)) → rectRMove8, centeroptionr8, b_2, c_2, d_2, e_2, f_3
  37. Polygon(R, S, T, U) → q4, r_3, s_3, t_3, u
  38. Text(optionsLActual(1), CenterOptionL1, true, true, 0, 0) → opL1
  39. Text(optionsLActual(2), CenterOptionL2, true, true, 0, 0) → opL2
  40. Text(optionsLActual(3), CenterOptionL3, true, true, 0, 0) → opL3
  41. Text(optionsLActual(4), CenterOptionL4, true, true, 0, 0) → opL4
  42. Text(optionsLActual(5), CenterOptionL5, true, true, 0, 0) → opL5
  43. PointIn(allowedRect) → CenterOptionR1
  44. Polygon(CenterOptionR1, CenterOptionR1 - (widthR / 2, heightR / 2), CenterOptionR1 + (widthR / 2, ((-heightR)) / 2), CenterOptionR1 + (widthR / 2, heightR / 2), CenterOptionR1 - (widthR / 2, ((-heightR)) / 2), CenterOptionR1 - (widthR / 2, heightR / 2)) → rectRMove1, centeroptionr1, f, g, h, i, j
  45. Text(optionsRActual(1), CenterOptionR1, true, true, 0, 0) → opR1
  46. PointIn(allowedRect) → CenterOptionR2
  47. Polygon(CenterOptionR2, CenterOptionR2 - (widthR / 2, heightR / 2), CenterOptionR2 + (widthR / 2, ((-heightR)) / 2), CenterOptionR2 + (widthR / 2, heightR / 2), CenterOptionR2 - (widthR / 2, ((-heightR)) / 2), CenterOptionR2 - (widthR / 2, heightR / 2)) → rectRMove2, centeroptionr2, k, l, m, n, p
  48. Text(optionsRActual(2), CenterOptionR2, true, true, 0, 0) → opR2
  49. PointIn(allowedRect) → CenterOptionR3
  50. Polygon(CenterOptionR3, CenterOptionR3 - (widthR / 2, heightR / 2), CenterOptionR3 + (widthR / 2, ((-heightR)) / 2), CenterOptionR3 + (widthR / 2, heightR / 2), CenterOptionR3 - (widthR / 2, ((-heightR)) / 2), CenterOptionR3 - (widthR / 2, heightR / 2)) → rectRMove3, centeroptionr3, q, r, s, t, e
  51. Text(optionsRActual(3), CenterOptionR3, true, true, 0, 0) → opR3
  52. PointIn(allowedRect) → CenterOptionR4
  53. Polygon(CenterOptionR4, CenterOptionR4 - (widthR / 2, heightR / 2), CenterOptionR4 + (widthR / 2, ((-heightR)) / 2), CenterOptionR4 + (widthR / 2, heightR / 2), CenterOptionR4 - (widthR / 2, ((-heightR)) / 2), CenterOptionR4 - (widthR / 2, heightR / 2)) → rectRMove4, centeroptionr4, f_1, g_1, h_1, i_1, j_1
  54. Text(optionsRActual(4), CenterOptionR4, true, true, 0, 0) → opR4
  55. PointIn(allowedRect) → CenterOptionR5
  56. Polygon(CenterOptionR5, CenterOptionR5 - (widthR / 2, heightR / 2), CenterOptionR5 + (widthR / 2, ((-heightR)) / 2), CenterOptionR5 + (widthR / 2, heightR / 2), CenterOptionR5 - (widthR / 2, ((-heightR)) / 2), CenterOptionR5 - (widthR / 2, heightR / 2)) → rectRMove5, centeroptionr5, m_1, n_1, p_1, b_1, c_1
  57. Text(optionsRActual(5), CenterOptionR5, true, true, 0, 0) → opR5
  58. PointIn(allowedRect) → CenterOptionR6
  59. Polygon(CenterOptionR6, CenterOptionR6 - (widthR / 2, heightR / 2), CenterOptionR6 + (widthR / 2, ((-heightR)) / 2), CenterOptionR6 + (widthR / 2, heightR / 2), CenterOptionR6 - (widthR / 2, ((-heightR)) / 2), CenterOptionR6 - (widthR / 2, heightR / 2)) → rectRMove6, centeroptionr6, d_1, k_2, l_2, m_2, n_2
  60. Text(optionsRActual(6), CenterOptionR6, true, true, 0, 0) → opR6
  61. PointIn(allowedRect) → CenterOptionR7
  62. Polygon(CenterOptionR7, CenterOptionR7 - (widthR / 2, heightR / 2), CenterOptionR7 + (widthR / 2, ((-heightR)) / 2), CenterOptionR7 + (widthR / 2, heightR / 2), CenterOptionR7 - (widthR / 2, ((-heightR)) / 2), CenterOptionR7 - (widthR / 2, heightR / 2)) → rectRMove7, centeroptionr7, p_2, q_2, r_2, s_2, t_2
  63. Text(optionsRActual(7), CenterOptionR7, true, true, 0, 0) → opR7
  64. If(CountIf[P ∈ answerRectLarger1(1), P, verticesR1] ≟ 4, 1, CountIf[P ∈ answerRectLarger6(1), P, verticesR1] ≟ 4, 6, CountIf[P ∈ answerRectLarger7(1), P, verticesR1] ≟ 4, 7, CountIf[P ∈ answerRectLarger8(1), P, verticesR1] ≟ 4, 8, -1, CountIf[P ∈ answerRectLarger2(1), P, verticesR1] ≟ 4, 2, CountIf[P ∈ answerRectLarger3(1), P, verticesR1] ≟ 4, 3, CountIf[P ∈ answerRectLarger4(1), P, verticesR1] ≟ 4, 4, CountIf[P ∈ answerRectLarger5(1), P, verticesR1] ≟ 4, 5) → indexAnswerR1
  65. If(CountIf[P ∈ answerRectLarger1(1), P, verticesR2] ≟ 4, 1, CountIf[P ∈ answerRectLarger6(1), P, verticesR2] ≟ 4, 6, CountIf[P ∈ answerRectLarger7(1), P, verticesR2] ≟ 4, 7, CountIf[P ∈ answerRectLarger8(1), P, verticesR2] ≟ 4, 8, -1, CountIf[P ∈ answerRectLarger2(1), P, verticesR2] ≟ 4, 2, CountIf[P ∈ answerRectLarger3(1), P, verticesR2] ≟ 4, 3, CountIf[P ∈ answerRectLarger4(1), P, verticesR2] ≟ 4, 4, CountIf[P ∈ answerRectLarger5(1), P, verticesR2] ≟ 4, 5) → indexAnswerR2
  66. If(CountIf[P ∈ answerRectLarger1(1), P, verticesR3] ≟ 4, 1, CountIf[P ∈ answerRectLarger6(1), P, verticesR3] ≟ 4, 6, CountIf[P ∈ answerRectLarger7(1), P, verticesR3] ≟ 4, 7, CountIf[P ∈ answerRectLarger8(1), P, verticesR3] ≟ 4, 8, -1, CountIf[P ∈ answerRectLarger2(1), P, verticesR3] ≟ 4, 2, CountIf[P ∈ answerRectLarger3(1), P, verticesR3] ≟ 4, 3, CountIf[P ∈ answerRectLarger4(1), P, verticesR3] ≟ 4, 4, CountIf[P ∈ answerRectLarger5(1), P, verticesR3] ≟ 4, 5) → indexAnswerR3
  67. If(CountIf[P ∈ answerRectLarger1(1), P, verticesR4] ≟ 4, 1, CountIf[P ∈ answerRectLarger6(1), P, verticesR4] ≟ 4, 6, CountIf[P ∈ answerRectLarger7(1), P, verticesR4] ≟ 4, 7, CountIf[P ∈ answerRectLarger8(1), P, verticesR4] ≟ 4, 8, -1, CountIf[P ∈ answerRectLarger2(1), P, verticesR4] ≟ 4, 2, CountIf[P ∈ answerRectLarger3(1), P, verticesR4] ≟ 4, 3, CountIf[P ∈ answerRectLarger4(1), P, verticesR4] ≟ 4, 4, CountIf[P ∈ answerRectLarger5(1), P, verticesR4] ≟ 4, 5) → indexAnswerR4
  68. If(CountIf[P ∈ answerRectLarger1(1), P, verticesR5] ≟ 4, 1, CountIf[P ∈ answerRectLarger6(1), P, verticesR5] ≟ 4, 6, CountIf[P ∈ answerRectLarger7(1), P, verticesR5] ≟ 4, 7, CountIf[P ∈ answerRectLarger8(1), P, verticesR5] ≟ 4, 8, -1, CountIf[P ∈ answerRectLarger2(1), P, verticesR5] ≟ 4, 2, CountIf[P ∈ answerRectLarger3(1), P, verticesR5] ≟ 4, 3, CountIf[P ∈ answerRectLarger4(1), P, verticesR5] ≟ 4, 4, CountIf[P ∈ answerRectLarger5(1), P, verticesR5] ≟ 4, 5) → indexAnswerR5
  69. If(CountIf[P ∈ answerRectLarger1(1), P, verticesR6] ≟ 4, 1, CountIf[P ∈ answerRectLarger6(1), P, verticesR6] ≟ 4, 6, CountIf[P ∈ answerRectLarger7(1), P, verticesR6] ≟ 4, 7, CountIf[P ∈ answerRectLarger8(1), P, verticesR6] ≟ 4, 8, -1, CountIf[P ∈ answerRectLarger2(1), P, verticesR6] ≟ 4, 2, CountIf[P ∈ answerRectLarger3(1), P, verticesR6] ≟ 4, 3, CountIf[P ∈ answerRectLarger4(1), P, verticesR6] ≟ 4, 4, CountIf[P ∈ answerRectLarger5(1), P, verticesR6] ≟ 4, 5) → indexAnswerR6
  70. If(CountIf[P ∈ answerRectLarger1(1), P, verticesR7] ≟ 4, 1, CountIf[P ∈ answerRectLarger6(1), P, verticesR7] ≟ 4, 6, CountIf[P ∈ answerRectLarger7(1), P, verticesR7] ≟ 4, 7, CountIf[P ∈ answerRectLarger8(1), P, verticesR7] ≟ 4, 8, -1, CountIf[P ∈ answerRectLarger2(1), P, verticesR7] ≟ 4, 2, CountIf[P ∈ answerRectLarger3(1), P, verticesR7] ≟ 4, 3, CountIf[P ∈ answerRectLarger4(1), P, verticesR7] ≟ 4, 4, CountIf[P ∈ answerRectLarger5(1), P, verticesR7] ≟ 4, 5) → indexAnswerR7
  71. If(CountIf[P ∈ answerRectLarger1(1), P, verticesR8] ≟ 4, 1, CountIf[P ∈ answerRectLarger6(1), P, verticesR8] ≟ 4, 6, CountIf[P ∈ answerRectLarger7(1), P, verticesR8] ≟ 4, 7, CountIf[P ∈ answerRectLarger8(1), P, verticesR8] ≟ 4, 8, -1, CountIf[P ∈ answerRectLarger2(1), P, verticesR8] ≟ 4, 2, CountIf[P ∈ answerRectLarger3(1), P, verticesR8] ≟ 4, 3, CountIf[P ∈ answerRectLarger4(1), P, verticesR8] ≟ 4, 4, CountIf[P ∈ answerRectLarger5(1), P, verticesR8] ≟ 4, 5) → indexAnswerR8
  72. CountIf(ind ≠ -1, ind, indizesAnswerR) → numAnswersDraggedToLeft
  73. If(correct, "\vphantom{✘}✓ Richtig", If[correctpartially, "\vphantom{✓}✘ Teilweise richtig", "\vphantom{✓}✘ Falsch"]) → correctTextTemp
  74. Text((("\Large\textsf{" * correctTextTemp) * "}"), PStartCorrectText, true, true, 1, 0) → correctText