分数扩展练习

分数扩展练习
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2022-08-10 19:27
该范例演示了分数扩展的概念,涉及的核心数学概念包括分数的基本性质和扩展方法。通过使用GeoGebra命令如Join、Sequence、Point等,学生可以直观地理解分数扩展的过程。适合小学五年级至六年级学生使用,帮助他们掌握分数扩展和简化的方法。

GeoGebra 命令及参数

  1. Join({{"$\textsf{\vphantom{Äg}\phantom{=}}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * AufgabenText(i)) * "}$"), i, 1, CountIf[x ≠ "" ∨ x ≠ 0, AufgabenText]]}) → LDP1
  2. Sequence(Random[2, 12], i, 1, 100) → randomNenner, {5, 2, 12, 2, 12, 10, 11, 12, 7, 4, 2, 8, 10, 6, 10, 12, 7, 9, 10, 6, 3, 10, 5, 12, 3, 2, 3, 5, 2, 8, 5, 12, 8, 5, 7, 7, 9, 7, 5, 11, 4, 11, 2, 2, 6, 2, 11, 6, 7, 4, 8, 9, 12, 11, 7, 8, 12, 2, 3, 7, 7, 2, 11, 11, 6, 12, 2, 6, 7, 7, 7, 5, 6, 6, 12, 5, 8, 3, 3, 8, 10, 12, 3, 7, 9, 4, 6, 3, 4, 8, 3, 8, 5, 10, 6, 10, 9, 2, 7, 7}
  3. Sequence(Random[2, nenner2 - 1], i, 1, 100) → randomZaehler, {7, 3, 5, 7, 2, 6, 6, 2, 3, 4, 6, 7, 4, 3, 3, 5, 7, 4, 3, 5, 5, 6, 4, 6, 7, 3, 6, 4, 2, 2, 5, 3, 6, 5, 2, 7, 3, 2, 7, 3, 5, 4, 7, 2, 5, 3, 7, 3, 6, 5, 6, 2, 7, 5, 6, 7, 5, 2, 2, 6, 7, 7, 5, 6, 5, 5, 6, 5, 4, 6, 2, 3, 2, 6, 4, 4, 3, 5, 4, 5, 7, 5, 7, 6, 6, 4, 5, 4, 7, 3, 7, 6, 3, 2, 4, 4, 2, 2, 2, 4}
  4. Sequence(I + ((i * widthNennerBar / 12) * (1, 0)), i, 1, 12) → allowedPositionsNennerBar
  5. Point(allowedPositionsNennerBar) → PNenner
  6. Circle(M, B) → c
  7. Segment(M, M + (Radius[c] * (0, 1))) → f
  8. Vector(F, G) → u
  9. Segment(H, H + (widthZaehlerBar * (1, 0))) → g
  10. Segment(I, I + (widthNennerBar * (1, 0))) → h
  11. Sequence(H + ((i * widthZaehlerBar / 12) * (1, 0)), i, 0, nenner2) → allowedPositionsZaehlerBar
  12. Point(allowedPositionsZaehlerBar) → PZaehler
  13. Sequence(Rotate[f, ((i * 2) * pi / nenner2), M], i, 0, nenner2 - 1) → l1
  14. Sequence(CircleSector[M, Rotate[KreisOben, (((-(i + 1)) * 2) * pi / nenner2), M], Rotate[KreisOben, (((-i) * 2) * pi / nenner2) - 0.0001, M]], i, 0, zaehler2 - 1) → l2
  15. Sequence(Random[1, zaehler2 - 1], i, 1, 100) → randomSubtrahend, {4, 1, 4, 3, 2, 2, 4, 3, 4, 1, 2, 4, 3, 2, 2, 2, 4, 4, 1, 3, 2, 2, 3, 2, 1, 2, 2, 4, 2, 3, 2, 1, 3, 4, 3, 1, 3, 1, 2, 2, 3, 2, 3, 4, 1, 4, 1, 1, 3, 4, 3, 4, 4, 1, 1, 4, 1, 4, 3, 1, 3, 4, 2, 1, 1, 3, 1, 1, 3, 1, 3, 3, 1, 3, 4, 2, 1, 1, 3, 4, 3, 3, 4, 4, 3, 4, 3, 4, 2, 3, 2, 4, 1, 2, 1, 2, 2, 4, 4, 1}
  16. Center(sektor12v1) → M12v1
  17. Center(sektor12v2) → M12v2
  18. Center(sektor12v3) → M12v3
  19. Center(sektor12v4) → M12v4
  20. Center(sektor12v5) → M12v5
  21. Center(sektor12v6) → M12v6
  22. Center(sektor12v7) → M12v7
  23. Center(sektor12v8) → M12v8
  24. Center(sektor12v9) → M12v9
  25. Center(sektor12v10) → M12v10
  26. Center(sektor12v11) → M12v11
  27. Center(sektor12v12) → M12v12
  28. Textfield(input1) → Eingabefeld1
  29. Textfield(input2) → Eingabefeld2
  30. Join({{"$\textsf{\vphantom{Äg}Wähle aus!}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * AufgabenText(i)) * "}$"), i, 1, CountIf[x ≠ "" ∨ x ≠ 0, AufgabenText]]}) → LDP1_{1}
  31. Join({{"$\textsf{\vphantom{Äg}Wähle aus!}$"}, Sequence[(("$\textsf{\vphantom{Äg}" * AufgabenText(i)) * "}$"), i, 1, CountIf[x ≠ "" ∨ x ≠ 0, AufgabenText]]}) → LDP2
  32. Point(xAxis) → J
  33. OrthogonalLine(J, xAxis) → i
  34. Point(xAxis) → K
  35. LineBisector(K, J) → j
  36. Translate({l2}, (dxBruch2, 0)) → showBruch201
  37. Sequence(Rotate[f, ((i * 2) * pi / ((verfeinerung * nenner2))), M], i, 0, (verfeinerung * nenner2) - 1) → l3
  38. Translate({l3}, (dxBruch2, 0)) → showBruch202
  39. Translate({c, l1}, (dxBruch2, 0)) → showBruch203
  40. LaTeX(step, true, true) → Text5
  41. CircleArc(O, N, PosBogerl) → bogerl11
  42. Point(bogerl11) → P
  43. Vector(P, N + (0.1 * Vector[P, N])) → bogerl1pfeil
  44. Translate({bogerl11, bogerl1pfeil}, (0, 0)) → bogen1
  45. OrthogonalLine(Q, yAxis) → k
  46. Mirror(bogen1(1), k) → bogen1'
  47. Point(bogen1') → R
  48. Point(bogen1') → S
  49. Vector(R, S + (0.1 * Vector[R, S])) → v
  50. Point(bogen1') → T
  51. If(step ≟ 3, SelectedIndex[LDP1] ≠ 1, false) → fixedSectors
  52. If(step ≟ 3, SelectedIndex[LDP1] ≟ 1, step ≟ 4, false, true) → showpart2

AI 绘图提示语参考

画一个分数扩展的示意图,展示分数的基本性质和方法。包含一个坐标轴,一个圆和多个扇形,扇形之间通过旋转和移动排列,形成分数的表示。圆的中心有一个点,圆上有点和线段,线段之间有特定的位置关系。扇形之间有重叠和间隔,整体构成一个分数的几何表示。先画出坐标轴和圆,再画出圆上的点和线段,然后旋转和移动扇形,最后调整位置关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。