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找到等价分数

找到等价分数
几何画板及绘图内容加载中，请稍等……
2022-08-10 19:38
不等式
所属专题 Bruchzahlen: Erweitern und Kürzen
这个 GeoGebra 范例演示了如何找到两个分数的等价分数。它涉及的核心数学概念是分数的比较和简化。作图要点包括使用 GeoGebra 的 Sequence、If 和 Join 命令来创建分数的图形。这个范例适合 5-6 年级学生，帮助他们理解和操作分数的概念。

GeoGebra 命令及参数

  1. Sequence(Random[2, 12], i, 1, 100) → randomNosNenner, {12, 6, 8, 6, 4, 4, 11, 5, 2, 2, 2, 9, 6, 6, 10, 7, 10, 10, 11, 7, 10, 8, 10, 7, 7, 12, 12, 2, 2, 3, 6, 3, 12, 8, 9, 3, 11, 2, 12, 12, 5, 5, 4, 12, 3, 11, 3, 11, 2, 10, 11, 7, 11, 10, 10, 4, 9, 3, 11, 5, 4, 2, 7, 7, 4, 2, 9, 6, 10, 5, 9, 2, 9, 5, 7, 12, 2, 2, 7, 7, 8, 8, 11, 2, 2, 2, 7, 9, 8, 7, 6, 2, 5, 9, 5, 10, 3, 11, 3, 6}
  2. Sequence(Random[1, nenner2 - 1], i, 1, 100) → randomNosZaehler, {2, 3, 1, 1, 3, 3, 2, 1, 2, 4, 3, 3, 3, 5, 1, 1, 2, 3, 2, 1, 4, 5, 2, 1, 5, 1, 3, 3, 4, 2, 2, 3, 4, 4, 3, 3, 5, 5, 3, 2, 5, 2, 3, 2, 3, 5, 5, 2, 2, 3, 2, 5, 5, 5, 5, 4, 2, 1, 3, 5, 1, 4, 1, 2, 3, 2, 5, 1, 3, 5, 3, 1, 1, 2, 1, 2, 1, 1, 3, 5, 3, 1, 3, 3, 1, 3, 5, 5, 1, 4, 3, 1, 3, 2, 2, 5, 2, 1, 5, 2}
  3. If(randomNosZaehler(questionCount) ≟ 0, 1, randomNosZaehler(questionCount)) → zaehler2
  4. Join({{0.25, 0.5}, Intersection[DivisorsList[nenner2], DivisorsList[zaehler2]]}) → durchschnittTeiler
  5. If(¬part2, Pos1, Pos2) → MidPoint
  6. Circle(MidPoint, pointKreis1) → kreis1
  7. Join({{"$\textsf{\vphantom{Äg}\phantom{=}}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * AufgabenText(i)) * "}$"), i, 1, CountIf[x ≠ "" ∨ x ≠ 0, AufgabenText]]}) → LDP1
  8. CountIf(x ≠ 0, durchschnittTeiler) → anzahlTeiler
  9. If(¬part2, correct1 ∧ correct2, correct3 ∧ correct4) → correct
  10. If(¬recSplit, (x(pointAreaLeft2), y(pointAreaLeft4)), pointAreaLeft4 + (((If[zaehler2 > nenner2 / 2, zaehler2 - nenner2 / 2, zaehler2] * 2) * dxRectangle / nenner2), 0)) → pointAreaLeft3
  11. Sequence(Random[2, 12], i, 1, 100) → randomNenner, {5, 8, 11, 12, 2, 12, 7, 3, 11, 8, 7, 11, 2, 9, 12, 11, 4, 2, 2, 6, 2, 12, 7, 5, 12, 9, 7, 5, 5, 9, 7, 2, 5, 4, 4, 11, 10, 7, 11, 6, 8, 11, 11, 5, 11, 6, 6, 10, 11, 9, 2, 3, 8, 10, 2, 10, 3, 10, 5, 9, 2, 10, 12, 7, 12, 6, 4, 6, 2, 6, 10, 4, 6, 10, 9, 8, 2, 2, 6, 4, 10, 8, 3, 4, 5, 11, 9, 5, 3, 2, 8, 7, 12, 12, 2, 10, 9, 5, 10, 7}
  12. Sequence(Random[2, nenner2 - 1], i, 1, 100) → randomZaehler, {2, 2, 4, 4, 5, 2, 2, 5, 4, 2, 4, 2, 3, 5, 4, 5, 5, 4, 5, 2, 5, 2, 2, 5, 5, 5, 2, 3, 3, 3, 3, 3, 2, 5, 4, 4, 3, 5, 3, 5, 5, 4, 5, 2, 3, 5, 5, 5, 2, 5, 2, 2, 5, 2, 5, 3, 2, 4, 5, 3, 5, 5, 3, 3, 5, 5, 2, 4, 4, 4, 3, 4, 2, 2, 2, 3, 5, 3, 4, 4, 2, 5, 3, 5, 4, 2, 3, 2, 3, 4, 5, 4, 2, 2, 4, 4, 3, 2, 4, 4}
  13. Sequence(I + ((i * widthNennerBar / 12) * (1, 0)), i, 1, 12) → allowedPositionsNennerBar
  14. Point(allowedPositionsNennerBar) → PNenner
  15. Circle(M, B) → c
  16. Segment(M, M + (Radius[c] * (0, 1))) → f
  17. Vector(F, G) → u
  18. Segment(H, H + (widthZaehlerBar * (1, 0))) → g
  19. Segment(I, I + (widthNennerBar * (1, 0))) → h
  20. Sequence(H + ((i * widthZaehlerBar / 12) * (1, 0)), i, 0, nenner2) → allowedPositionsZaehlerBar
  21. Point(allowedPositionsZaehlerBar) → PZaehler
  22. Sequence(Rotate[f, ((i * 2) * pi / nenner2), M], i, 0, nenner2 - 1) → listAreaLeft_{1}
  23. Sequence(CircleSector[MidPoint, Rotate[KreisOben, (((-(i + 1)) * 2) * pi / nenner2), MidPoint], Rotate[KreisOben, (((-i) * 2) * pi / nenner2) - 0.0001, MidPoint]], i, 0, zaehler2 - 1) → listAreaLeftCircle
  24. Sequence(Random[1, zaehler2 - 1], i, 1, 100) → randomSubtrahend, {1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2}
  25. Center(sektor12v1) → M12v1
  26. Center(sektor12v2) → M12v2
  27. Center(sektor12v3) → M12v3
  28. Center(sektor12v4) → M12v4
  29. Center(sektor12v5) → M12v5
  30. Center(sektor12v6) → M12v6
  31. Center(sektor12v7) → M12v7
  32. Center(sektor12v8) → M12v8
  33. Center(sektor12v9) → M12v9
  34. Center(sektor12v10) → M12v10
  35. Center(sektor12v11) → M12v11
  36. Center(sektor12v12) → M12v12
  37. Textfield(input1) → Eingabefeld1
  38. Textfield(input2) → Eingabefeld2
  39. Join({{"$\textsf{\vphantom{Äg}Wähle aus!}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * AufgabenText(i)) * "}$"), i, 1, CountIf[x ≠ "" ∨ x ≠ 0, AufgabenText]]}) → LDP1_{1}
  40. Join({{"$\textsf{\vphantom{Äg}Wähle aus!}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * AufgabenText(i)) * "}$"), i, 1, CountIf[x ≠ "" ∨ x ≠ 0, AufgabenText]]}) → LDP2
  41. Point(xAxis) → J
  42. OrthogonalLine(J, xAxis) → i
  43. Point(xAxis) → K
  44. LineBisector(K, J) → j
  45. Translate({listAreaLeftCircle}, (dxBruch2, 0)) → showBruch201
  46. Sequence(Rotate[f, ((i * 2) * pi / ((verfeinerung * nenner2))), M], i, 0, (verfeinerung * nenner2) - 1) → l3
  47. Translate({l3}, (dxBruch2, 0)) → showBruch202
  48. Translate({c, listAreaLeft_{1}}, (dxBruch2, 0)) → showBruch203
  49. LaTeX(step, true, true) → Text5
  50. CircleArc(O, N, PosBogerl) → bogerl11
  51. Point(bogerl11) → pointBogerl1
  52. Vector(pointBogerl1, N + (0.1 * Vector[pointBogerl1, N])) → bogerl1pfeil
  53. OrthogonalLine(Q, yAxis) → k
  54. Sequence(7) → listSteps
  55. Min(listSteps) → Min
  56. Max(listSteps) → Maximum
  57. Segment(pointFrame3, pointFrame2) → lineLeftHorizontal
  58. Segment(pointFrame2, pointFrame1) → lineLeftVertical
  59. Join({Sequence[Segment[Translate[pointFrame2, (i * If[nenner2 ≟ 2, (i * dxRectangle / nenner2), ((dxRectangle * If[Mod[nenner2, 2] ≟ 0, 2, 1] / nenner2), 0)])], Translate[pointFrame1, (i * If[nenner2 ≟ 2, (i * dxRectangle / nenner2), ((dxRectangle * If[Mod[nenner2, 2] ≟ 0, 2, 1] / nenner2), 0)])]], i, 0, (nenner2 * If[Mod[nenner2, 2] ≟ 0, 0.5, 1])], Sequence[Segment[Translate[pointFrame3, (i * If[Mod[nenner2, 2] ≟ 0 ∧ nenner2 ≠ 2, (0, dyRectangle / 2), (0, dyRectangle)])], Translate[pointFrame2, (i * If[Mod[nenner2, 2] ≟ 0 ∧ nenner2 ≠ 2, (0, dyRectangle / 2), (0, dyRectangle)])]], i, 0, If[Mod[nenner2, 2] ≟ 0 ∧ nenner2 ≠ 2, 2, 1]]}) → listLeftLinesVertical
  60. Join({{lineLeftHorizontal, lineLeftVertical}, {Segment[Translate[pointFrame3, (0, dyRectangle)], Translate[pointFrame2, (0, dyRectangle)]]}, {Segment[Translate[pointFrame2, (dxRectangle, 0)], Translate[pointFrame1, (dxRectangle, 0)]]}}) → listFrameLeft
  61. Translate(listFrameLeft, (dxShift, 0)) → listFrameRight
  62. Translate(listAreaLeft, (dxShift, 0)) → listAreaRight
  63. Intersection(DivisorsList[zaehler2], DivisorsList[nenner2]) → l1
  64. Join({Sequence[Translate[Segment[Translate[pointFrame2, (dxShift, 0)], Translate[pointFrame1, (dxShift, 0)]], (i * If[nenner3 ≟ 2, (i * dxRectangle / nenner3), ((dxRectangle * If[Mod[nenner3, 2] ≟ 0, 2, 1] / nenner3), 0)])], i, 0, (nenner3 * If[Mod[nenner3, 2] ≟ 0, 0.5, 1])], Sequence[Translate[Segment[Translate[pointFrame3, (dxShift, 0)], Translate[pointFrame2, (dxShift, 0)]], (i * If[Mod[nenner3, 2] ≟ 0 ∧ nenner3 ≠ 2, (0, dyRectangle / 2), (0, dyRectangle)])], i, 0, If[Mod[nenner3, 2] ≟ 0 ∧ nenner3 ≠ 2, 2, 1]]}) → l4
  65. If(¬recSplit2, (x(pointAreaRight2), y(pointAreaRight4)), pointAreaRight4 + (((If[zaehler3 > nenner3 / 2, zaehler3 - nenner3 / 2, zaehler3] * 2) * dxRectangle / nenner3), 0)) → pointAreaRight3
  66. OrthogonalLine(L, yAxis) → l
  67. Mirror(bogerl11, l) → bogerl12
  68. Mirror(pointBogerl1, l) → pointBogerl2
  69. Sequence(Segment[Rotate[MidPoint, ((i * 2) * pi / nenner2), MidPoint], Rotate[pointKreis1, ((i * 2) * pi / nenner2), MidPoint]], i, 0, nenner2 - 1) → listLinesCircleLeft1
  70. Sequence(Segment[Rotate[MidPoint2, ((i * 2) * pi / nenner3), MidPoint2], Rotate[KreisOben2, ((i * 2) * pi / nenner3), MidPoint2]], i, 0, nenner3 - 1) → listLinesCircleRight
  71. Circle(MidPoint2, radius) → kreis2
  72. Sequence(CircleSector[MidPoint2, Rotate[KreisOben2, (((-(i + 1)) * 2) * pi / nenner3), MidPoint2], Rotate[KreisOben2, (((-i) * 2) * pi / nenner3) - 0.0001, MidPoint2]], i, 0, zaehler3 - 1) → listAreaRightCircle
  73. Rotate(KreisOben, ((-zaehler2) * (360°) / nenner2), MidPoint) → KreisEckpunkt
  74. CircleSector((-5.766287229319031, 3.8699043461027944), (-5.766287229319031, 1.5199043461027948), (-5.766287229319031, 6.219904346102794)) → listAreaLeftCircle2
  75. Textfield(input3) → Eingabefeld3
  76. Textfield(input4) → Eingabefeld4
  77. Textfield(input1) → zwEingabefeld1
  78. Textfield(input2) → zwEingabefeld2

AI 绘图提示语参考

画两个分数条形/圆形区域的对比练习：先在同一张画面中准备一个标注为“选择”并含多项填空的交互区域，让用户输入或选择分数答案。图的主体用两个同分母划分的圆扇形表示一个分数，其中圆心固定，圆被均分为若干等分；再用同样的分割方式在旁边展示另一个分数。分别强调两处分数对应的等分面积与交集处的共同部分，把它们与分子、分母的大小关系联系起来。最后给出用于判断正确性的提示文本区域。
以上提示语为根据原始绘图命令整理而来，仅供参考。