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假分数可视化演示：从圆与扇形到数轴表示

假分数可视化演示：从圆与扇形到数轴表示
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2018-09-25 18:50
圆几何作图滑块动画
① 本范例通过GeoGebra动态展示假分数（如分子大于分母的分数）的几何表示，将分数转化为圆、扇形、线段与数轴上的点，直观呈现其数值大小与组成。② 核心数学概念包括假分数与带分数的转换、分数的数轴定位、单位“1”的等分与累加，以及分数与几何图形（圆、扇形、线段）的对应关系。③ 作图要点：从构造摘要可见，使用了Rotate（旋转）、Intersect（求交点）、Point（点）、Line（线）、Vector（向量）、Sequence（序列）、Mod（取模）、Div（整除）、Circle（圆）、Segment（线段）、CircleSector（扇形）等命令，并创建了F1至F10等多个分数对象、分子（Numerator）与分母（Denominator）滑块、列表list1与list2以及多个文本标签（text1至text9），通过动态调整分子分母实时更新图形。④ 适合小学高年级至初中阶段学习分数概念、分数与几何直观联系，也可用于教师课堂演示或学生自主探索假分数与带分数的关系。

GeoGebra 命令及参数

  1. Rotate(F1, (2 * π / Denominator), F) → F2
  2. Rotate(F2, (2 * π / Denominator), F) → F3
  3. Rotate(F3, (2 * π / Denominator), F) → F4
  4. Rotate(F4, (2 * π / Denominator), F) → F5
  5. Rotate(F5, (2 * π / Denominator), F) → F6
  6. Rotate(F6, (2 * π / Denominator), F) → F7
  7. Rotate(F7, (2 * π / Denominator), F) → F8
  8. Rotate(F8, (2 * π / Denominator), F) → F9
  9. Rotate(F9, (2 * π / Denominator), F) → F10
  10. Intersect(xAxis, yAxis) → A
  11. Point(xAxis) → B
  12. Line(A, B) → a
  13. Vector(C, D) → u
  14. Sequence((d, 0), d, 0, 100, Zoom) → list1
  15. Mod(Numerator, Denominator) → c
  16. Div(Numerator, Denominator) → e
  17. Sequence((d, 0), d, 0, 36, b) → list2
  18. Circle(F, 4) → f
  19. Circle(G, 4) → g
  20. Circle(H, 4) → h
  21. Rotate(F10, (2 * π / Denominator), F) → F11
  22. Segment(F, F1) → i
  23. Segment(F, F2) → j
  24. Segment(F, F3) → k
  25. Segment(F, F4) → l
  26. Segment(F, F5) → m
  27. Segment(F, F6) → n
  28. Segment(F, F7) → p
  29. Segment(F, F8) → q
  30. Segment(F, F9) → r
  31. Segment(F, F10) → s
  32. Rotate(F1, ((2 * π) * Numerator / Denominator), F) → F'
  33. CircleSector(F, F1, F') → c_1
  34. Circle(F, F1) → c_f
  35. Rotate(G1, (2 * π / Denominator), G) → G2
  36. Rotate(G2, (2 * π / Denominator), G) → G3
  37. Rotate(G3, (2 * π / Denominator), G) → G4
  38. Rotate(G4, (2 * π / Denominator), G) → G5
  39. Rotate(G5, (2 * π / Denominator), G) → G6
  40. Rotate(G6, (2 * π / Denominator), G) → G7
  41. Rotate(G7, (2 * π / Denominator), G) → G8
  42. Segment(F, F11) → f_1
  43. Rotate(G8, (2 * π / Denominator), G) → G9
  44. Rotate(G9, (2 * π / Denominator), G) → G10
  45. Rotate(G10, (2 * π / Denominator), G) → G11
  46. Rotate(H1, (2 * π / Denominator), H) → H2
  47. Rotate(H2, (2 * π / Denominator), H) → H3
  48. Rotate(H3, (2 * π / Denominator), H) → H4
  49. Rotate(H4, (2 * π / Denominator), H) → H5
  50. Rotate(H5, (2 * π / Denominator), H) → H6
  51. Rotate(H6, (2 * π / Denominator), H) → H7
  52. Rotate(H7, (2 * π / Denominator), H) → H8
  53. Rotate(H8, (2 * π / Denominator), H) → H9
  54. Rotate(H9, (2 * π / Denominator), H) → H10
  55. Rotate(H10, (2 * π / Denominator), H) → H11
  56. Rotate(F11, (2 * π / Denominator), F) → F12
  57. Segment(F, F12) → t
  58. Rotate(G11, (2 * π / Denominator), G) → G12
  59. Rotate(H11, (2 * π / Denominator), H) → H12
  60. Segment(G, G1) → g_1
  61. Segment(G, G2) → h_1
  62. Segment(G, G3) → i_1
  63. Segment(G, G4) → j_1
  64. Segment(G, G5) → k_1
  65. Segment(G, G6) → l_1
  66. Segment(G, G7) → m_1
  67. Segment(G, G8) → n_1
  68. Segment(G, G9) → p_1
  69. Segment(G, G10) → q_1
  70. Segment(G, G11) → r_1
  71. Segment(G, G12) → s_1
  72. Segment(H, H1) → t_1
  73. Segment(H, H2) → a_1
  74. Segment(H, H3) → b_1
  75. Segment(H, H4) → d_1
  76. Segment(H, H5) → e_1
  77. Segment(H, H6) → f_2
  78. Segment(H, H7) → g_2
  79. Segment(H, H8) → h_2
  80. Segment(H, H9) → i_2
  81. Segment(H, H10) → j_2
  82. Segment(H, H11) → k_2
  83. Segment(H, H12) → l_2
  84. Segment(F_1, F1_1) → i_3
  85. Circle(G, G1) → G_C
  86. Segment(G_2, G1_1) → g_3
  87. Circle(H, H1) → H_1
  88. Rotate(G1, ((2 * π) * Numerator / Denominator), G) → G'
  89. Rotate(H1, ((2 * π) * (Numerator - Denominator) / Denominator), H) → H'
  90. CircleSector(G, G1, G') → c_2
  91. CircleSector(H, H1, H') → d_2

AI 绘图提示语参考

绘制一个动态可视化假分数的图形：以三个等大的圆为基础，每个圆被等分为若干扇形，扇形的数量由分母决定。第一个圆用彩色扇形突出显示分子对应的部分，第二个圆显示完整的分母等分，第三个圆则展示额外的部分。同时，在下方绘制一条数轴，用点标记出假分数对应的位置，并用线段连接圆与数轴上的对应点，直观展示假分数与带分数的关系。所有图形随分子和分母的滑块变化而实时更新。
以上提示语为根据原始绘图命令整理而来，仅供参考。