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两个真分数的多种模型展示

两个真分数的多种模型展示
几何画板及绘图内容加载中，请稍等……
2013-06-05 04:32
数列变换几何作图
所属专题 fifth grade fractions
本范例展示了两个不同真分数的多种表示方法，包括线性图、数轴、集合等。通过这些不同的表示方式，学生可以更好地理解真分数的概念及其几何意义。构造过程中使用了Point, Min, If, Vector, Rotate, CircleSector, Segment, Polygon, Sequence, Circle, FractionText等GeoGebra命令。适合小学高年级至初中学生使用，有助于培养学生的几何直观和数学思维。

GeoGebra 命令及参数

  1. Point(Circle[R_1, 0.12]) → C_2
  2. Min(9 / denom1, 1) → a9
  3. Min(4 / denom1, 1) → a4
  4. Min(5 / denom1, 1) → a5
  5. Min(8 / denom1, 1) → a8
  6. Min(7 / denom1, 1) → a7
  7. Min(6 / denom1, 1) → a6
  8. Min(1 / denom1, 1) → a1
  9. Min(2 / denom1, 1) → a2
  10. If(denom1 < 10, " " + denom1, "" + denom1) → formatd
  11. Min(3 / denom1, 1) → a3
  12. Min(10 / denom1, 1) → a10
  13. Point(Circle[M, 1]) → Q
  14. Point(Circle[N, 1]) → R
  15. Point(Circle[L_1, 0.02]) → U_1
  16. Point(Circle[U_1, 0.5]) → V_1
  17. If(impr > 1, 1, 0) → Rect_{show}
  18. Vector(NL_c, NL_l) → u
  19. Vector(NL_c, NL_r) → v
  20. If(num1 / denom1 > 1, 1, 0) → Set_{show}
  21. Rotate(C_2, angle, R_1) → D_2
  22. CircleSector(R_1, C_2, D_2) → circle1_{sector}
  23. Rotate(C_2, (360 / denom1)°, R_1) → B_2
  24. Segment(K_2, L_2) → a_2
  25. Vector((0, 0.25), (0.1, 0.25)) → image_{vector}
  26. Polygon((0, 0.38), ((0.5 * num1 / denom1), 0.38), ((0.5 * num1 / denom1), 0.58), (0, 0.58)) → frac1area3_{shaded}, j_1, k_1, l_1, m_1
  27. Segment((1, 0.43), (1, 0.47)) → i_2
  28. Sequence(Segment[((1 / frac1linediv * i), 0.43), ((1 / frac1linediv * i), 0.47)], i, 1, frac1linediv) → frac1numLineHash
  29. Segment((0, 0.42), (0, 0.48)) → t_1
  30. Segment((1, 0.42), (1, 0.48)) → a
  31. Polygon((0, 0.38), (num1 / 10, 0.38), (num1 / 10, 0.58), (0, 0.58)) → frac1area2_{shaded}, b, c, d, e
  32. Sequence(Segment[(i / denom1, 0.42), (i / denom1, 0.48)], i, 1, denom1 - 1) → frac1linearModelDivisions
  33. Polygon((0, 0.42), (num1 / denom1, 0.42), (num1 / denom1, 0.48), (0, 0.48)) → frac1linear_{shaded}, f, g, h, i
  34. Sequence(Translate[Circle[(0.05, 0.48), 0.045], Vector[(0, 0), ((0.1 * i), 0)]], i, 0, denom1 - 1) → frac1OpenCircles
  35. Sequence(Translate[Circle[(0.05, 0.48), 0.04], Vector[(0, 0), ((0.1 * i), 0)]], i, 0, num1 - 1) → frac1setClosed
  36. Sequence(Segment[Rotate[(0.1504, 0.2), (360 / denom1)°, (0.1504, 0.2)], Rotate[(0.1504, 0.31), ((360 * i) * ° / denom1), (0.1504, 0.2)]], i, 0, denom2 - 1) → Circle2_{model-divisions}
  37. Circle((0.15, 0.2), 0.12) → Circle2_{outline}
  38. Sequence(Segment[Rotate[(0.15, 0.2), ((360 / denom1 * i))°, (0.15, 0.2)], Rotate[(0.15, 0.32), ((360 * i / denom2))°, (0.15, 0.2)]], i, 0, denom2) → circle2_{div}
  39. Circle((0.15, 0.475), 0.12) → Circle1_{outline}
  40. Sequence(Segment[Rotate[(0.15, 0.475), ((360 / denom1 * i))°, (0.15, 0.475)], Rotate[(0.15, 0.595), ((360 * i / denom1))°, (0.15, 0.475)]], i, 0, denom1) → circle1_{div}
  41. CircleSector((0.15, 0.2), (0.15, 0.32), Rotate[(0.15, 0.32), ((360 * num2 / denom2))°, (0.15, 0.2)]) → p
  42. Polygon((0, 0.38), (denom1 / 10, 0.38), (denom1 / 10, 0.58), (0, 0.58)) → frac1area2_{outline}, r, s, t, a_1
  43. Sequence(Segment[(i / 10, 0.38), (i / 10, 0.58)], i, 1, denom1 - 1) → frac1area_{div}
  44. Polygon((0, 0.1), (denom2 / 10, 0.1), (denom2 / 10, 0.3), (0, 0.3)) → frac2area2_{outline}, j, l, n, q
  45. Sequence(Segment[(i / 10, 0.1), (i / 10, 0.3)], i, 1, denom2 - 1) → frac2area_{div}
  46. Polygon((0, 0.1), (num2 / 10, 0.1), (num2 / 10, 0.3), (0, 0.3)) → frac2area2_{shaded}, b_1, c_1, d_1, e_1
  47. Polygon((0, 0.38), (0.5, 0.38), (0.5, 0.58), (0, 0.58)) → frac1area3_{outline}, f_1, g_1, h_1, i_1
  48. Polygon((0, 0.1), (0.5, 0.1), (0.5, 0.3), (0, 0.3)) → frac2area3_{outline}, n_1, p_1, q_1, r_1
  49. Sequence(Segment[((0.5 / denom1 * i), 0.38), ((0.5 / denom1 * i), 0.58)], i, 1, denom1 - 1) → frac1area3_{div}
  50. Sequence(Segment[((0.5 / denom2 * i), 0.1), ((0.5 / denom2 * i), 0.3)], i, 1, denom2 - 1) → frac2area3_{div}
  51. Polygon((0, 0.1), ((0.5 * num2 / denom2), 0.1), ((0.5 * num2 / denom2), 0.3), (0, 0.3)) → frac2area3_{shaded}, s_1, b_2, c_2, d_2
  52. Sequence(Translate[Circle[(0.05, 0.2), 0.04], Vector[(0, 0), ((0.1 * i), 0)]], i, 0, num2 - 1) → frac2setClosed
  53. Sequence(Translate[Circle[(0.05, 0.2), 0.045], Vector[(0, 0), ((0.1 * i), 0)]], i, 0, denom2 - 1) → frac2setOpen
  54. Vector(NL_c + (0, -0.27), NL_l + (0, -0.27)) → u_1
  55. Vector(NL_c + (0, -0.27), NL_r + (0, -0.27)) → v_1
  56. Segment((0, 0.43), (0, 0.47)) → f_2
  57. Segment((0, 0.16), (0, 0.2)) → e_2
  58. Segment((1, 0.16), (1, 0.2)) → g_2
  59. Sequence(Segment[((1 / frac2linediv * i), 0.16), ((1 / frac2linediv * i), 0.2)], i, 1, frac2linediv) → frac2numLineHash
  60. Vector(Frac2NumLnPt + (0, 0.05), Frac2NumLnPt) → frac2NumLnPtVector
  61. Vector(Frac1NumLnPt + (0, 0.05), Frac1NumLnPt) → frac1NumLnPtVector
  62. FractionText(1 / frac2linediv) → model2NumLnIntervalValue
  63. FractionText(1 / frac1linediv) → model1NumLnIntervalValue
  64. Segment(K_2 + (0, -0.27), L_2 + (0, -0.27)) → h_2
  65. Sequence(Segment[(i / denom2, 0.15), (i / denom2, 0.21)], i, 1, denom2 - 1) → frac2linearModelDivisions
  66. Segment((1, 0.15), (1, 0.21)) → j_2
  67. Segment((0, 0.15), (0, 0.21)) → k_2
  68. Polygon((0, 0.15), (num2 / denom2, 0.15), (num2 / denom2, 0.21), (0, 0.21)) → frac2linear_{shaded}, l_2, m_2, n_2, p_2
  69. Sequence(Polygon[(-0.455, 0.117 + k), (-0.195, 0.117 + k), (-0.195, 0.31 + k), (-0.455, 0.31 + k)], k, 0, 0.276, 0.276) → grayBoxes
  70. Sequence(Segment[(-0.435, 0.189 + k), (-0.397, 0.189 + k)], k, 0, 0.276, 0.276) → fracVinculum

AI 绘图提示语参考

绘制两个真分数的多种表示形式，包括线性、数轴和集合模型。首先画两个圆，分别表示两个分数的集合模型。接着画两个数轴，分别表示两个分数的线性模型。然后画两个扇形，分别表示两个分数的几何模型。最后，用矩形和多边形表示每个分数的阴影区域。
以上提示语为根据原始绘图命令整理而来，仅供参考。