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分数条加法演示

分数条加法演示
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2017-06-16 16:12
几何作图滑块动画函数图像
①本范例通过水平矩形区域模型（分数条）演示两个分数的加法运算；②涉及的核心数学概念包括分数加法、分数模型、几何表示；③作图要点——使用了GeoGebra命令FractionText, Polygon, Sequence, Segment；对象包括a, b, c, d, FractionSimplified, FracStripAB1Whole, FracStripAB2Whole, FracStripAB3Whole等；④适合初中数学教学，用于直观理解分数加法运算。

GeoGebra 命令及参数

  1. FractionText((a * d + c * b) / (b * d)) → FractionSimplified
  2. Polygon((0, 8.1), (4, 8.1), (4, 8.9), (0, 8.9)) → FracStripAB1Whole, h, i, j, k
  3. Polygon((6, 8.1), (10, 8.1), (10, 8.9), (6, 8.9)) → FracStripAB2Whole, p, q, r, s
  4. Polygon((0, 8.1), (If[a / b < 1, 4 * a / b, 4], 8.1), (If[a / b < 1, 4 * a / b, 4], 8.9), (0, 8.9)) → FracStripAB1Part, e, l, m, n
  5. Polygon((0, 7.1), (4, 7.1), (4, 7.9), (0, 7.9)) → FracStripAB3Whole, c_1, d_1, e_1, f_1
  6. Polygon((6, 8.1), (If[a / b < 2, 6 + 4 * (a / b - 1), 10], 8.1), (If[a / b < 2, 6 + 4 * (a / b - 1), 10], 8.9), (6, 8.9)) → FracStripAB2Part, g, t, a_1, b_1
  7. Polygon((0, 7.1), (If[a / b < 3, 4 * (a / b - 2), 4], 7.1), (If[a / b < 3, 4 * (a / b - 2), 4], 7.9), (0, 7.9)) → FracStripAB3Part, g_1, h_1, i_1, j_1
  8. Polygon((6, 7.1), (10, 7.1), (10, 7.9), (6, 7.9)) → FracStripAB4Whole, k_1, l_1, m_1, n_1
  9. Polygon((6, 7.1), (If[a / b < 4, 6 + 4 * (a / b - 3), 10], 7.1), (If[a / b < 4, 6 + 4 * (a / b - 3), 10], 7.9), (6, 7.9)) → FracStripAB4Part, p_1, q_1, r_1, s_1
  10. Polygon((0, 6.1), (4, 6.1), (4, 6.9), (0, 6.9)) → FracStripAB5Whole, t_1, a_2, b_2, c_2
  11. Polygon((0, 6.1), (If[a / b < 5, 4 * (a / b - 4), 4], 6.1), (If[a / b < 5, 4 * (a / b - 4), 4], 6.9), (0, 6.9)) → FracStripAB5Part, d_2, e_2, f_2, g_2
  12. Polygon((6, 4.1), (10, 4.1), (10, 4.9), (6, 4.9)) → FracStripAB10Whole, l_2, m_2, n_2, p_2
  13. Polygon((0, 5.1), (4, 5.1), (4, 5.9), (0, 5.9)) → FracStripAB7Whole, h_2, i_2, j_2, k_2
  14. Polygon((6, 5.1), (10, 5.1), (10, 5.9), (6, 5.9)) → FracStripAB8Whole, q_2, r_2, s_2, t_2
  15. Polygon((6, 6.1), (10, 6.1), (10, 6.9), (6, 6.9)) → FracStripAB6Whole, a_3, b_3, c_3, d_3
  16. Polygon((0, 4.1), (4, 4.1), (4, 4.9), (0, 4.9)) → FracStripAB9Whole, e_3, f_3, g_3, h_3
  17. Polygon((0, 5.1), (If[a / b < 7, 4 * (a / b - 6), 4], 5.1), (If[a / b < 7, 4 * (a / b - 6), 4], 5.9), (0, 5.9)) → FracStripAB7Part, i_3, j_3, k_3, l_3
  18. Polygon((6, 6.1), (If[a / b < 6, 6 + 4 * (a / b - 5), 10], 6.1), (If[a / b < 6, 6 + 4 * (a / b - 5), 10], 6.9), (6, 6.9)) → FracStripAB6Part, m_3, n_3, p_3, q_3
  19. Polygon((6, 5.1), (10, 5.1), (10, 5.9), (6, 5.9)) → FracStripAB8Part, r_3, s_3, t_3, a_4
  20. Polygon((0, 4.1), (4, 4.1), (4, 4.9), (0, 4.9)) → FracStripAB9Part, b_4, c_4, d_4, e_4
  21. Polygon((6, 4.1), (10, 4.1), (10, 4.9), (6, 4.9)) → FracStripAB10Part, f_4, g_4, h_4, i_4
  22. Polygon((0, 3.1), (If[c / d < 1, 4 * c / d, 4], 3.1), (If[c / d < 1, 4 * c / d, 4], 3.9), (0, 3.9)) → FracStripCD1Part, j_4, k_4, l_4, m_4
  23. Polygon((0, 3.1), (4, 3.1), (4, 3.9), (0, 3.9)) → FracStripCD1Whole, n_4, p_4, q_4, r_4
  24. Polygon((6, 3.1), (10, 3.1), (10, 3.9), (6, 3.9)) → FracStripCD2Whole, s_4, t_4, a_5, b_5
  25. Polygon((6, 3.1), (If[c / d < 2, 6 + 4 * (c / d - 1), 10], 3.1), (If[c / d < 2, 6 + 4 * (c / d - 1), 10], 3.9), (6, 3.9)) → FracStripCD2Part, c_5, d_5, e_5, f_5
  26. Polygon((0, 2.1), (4, 2.1), (4, 2.9), (0, 2.9)) → FracStripCD3Whole, g_5, h_5, i_5, j_5
  27. Polygon((6, 2.1), (10, 2.1), (10, 2.9), (6, 2.9)) → FracStripCD4Whole, k_5, l_5, m_5, n_5
  28. Polygon((0, 1.1), (4, 1.1), (4, 1.9), (0, 1.9)) → FracStripCD5Whole, p_5, q_5, r_5, s_5
  29. Polygon((6, 1.1), (10, 1.1), (10, 1.9), (6, 1.9)) → FracStripCD6Whole, t_5, a_6, b_6, c_6
  30. Polygon((0, 0.1), (4, 0.1), (4, 0.9), (0, 0.9)) → FracStripCD7Whole, d_6, e_6, f_6, g_6
  31. Polygon((6, -0.1), (10, -0.1), (10, -0.9), (6, -0.9)) → FracStripCD10Whole, h_6, i_6, j_6, k_6
  32. Polygon((6, 0.1), (10, 0.1), (10, 0.9), (6, 0.9)) → FracStripCD8Whole, l_6, m_6, n_6, p_6
  33. Polygon((0, -0.1), (4, -0.1), (4, -0.9), (0, -0.9)) → FracStripCD9Whole, q_6, r_6, s_6, t_6
  34. Polygon((0, 2.1), (If[c / d < 3, 4 * (c / d - 2), 4], 2.1), (If[c / d < 3, 4 * (c / d - 2), 4], 2.9), (0, 2.9)) → FracStripCD3Part, a_7, b_7, c_7, d_7
  35. Polygon((6, 2.1), (If[c / d < 4, 6 + 4 * (c / d - 3), 10], 2.1), (If[c / d < 4, 6 + 4 * (c / d - 3), 10], 2.9), (6, 2.9)) → FracStripCD4Part, e_7, f_7, g_7, h_7
  36. Polygon((6, 1.1), (10, 1.1), (10, 1.9), (6, 1.9)) → FracStripCD6Part, m_7, n_7, p_7, q_7
  37. Polygon((0, 1.1), (If[c / d < 5, 4 * (c / d - 4), 4], 1.1), (If[c / d < 5, 4 * (c / d - 4), 4], 1.9), (0, 1.9)) → FracStripCD5Part, i_7, j_7, k_7, l_7
  38. Polygon((0, 0.1), (4, 0.1), (4, 0.9), (0, 0.9)) → FracStripCD7Part, r_7, s_7, t_7, a_8
  39. Polygon((6, 0.1), (10, 0.1), (10, 0.9), (6, 0.9)) → FracStripCD8Part, b_8, c_8, d_8, e_8
  40. Polygon((0, -0.1), (4, -0.1), (4, -0.9), (0, -0.9)) → FracStripCD9Part, f_8, g_8, h_8, i_8
  41. Polygon((6, -0.1), (10, -0.1), (10, -0.9), (6, -0.9)) → FracStripCD10Part, j_8, k_8, l_8, m_8
  42. Sequence(Segment[(4 / If[cp, parts, b] * i, 8.1), (4 / If[cp, parts, b] * i, 8.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB1Partitions
  43. Sequence(Segment[(6 + 4 / If[cp, parts, b] * i, 8.1), (6 + 4 / If[cp, parts, b] * i, 8.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB2Partitions
  44. Sequence(Segment[(4 / If[cp, parts, b] * i, 7.1), (4 / If[cp, parts, b] * i, 7.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB3Partitions
  45. Sequence(Segment[(6 + 4 / If[cp, parts, b] * i, 7.1), (6 + 4 / If[cp, parts, b] * i, 7.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB4Partitions
  46. Sequence(Segment[(4 / If[cp, parts, b] * i, 6.1), (4 / If[cp, parts, b] * i, 6.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB5Partitions
  47. Sequence(Segment[(4 / If[cp, parts, d] * i, 3.1), (4 / If[cp, parts, d] * i, 3.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD1Partitions
  48. Sequence(Segment[(6 + 4 / If[cp, parts, d] * i, 3.1), (6 + 4 / If[cp, parts, d] * i, 3.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD2Partitions
  49. Sequence(Segment[(4 / If[cp, parts, d] * i, 2.1), (4 / If[cp, parts, d] * i, 2.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD3Partitions
  50. Sequence(Segment[(6 + 4 / If[cp, parts, d] * i, 2.1), (6 + 4 / If[cp, parts, d] * i, 2.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD4Partitions
  51. Sequence(Segment[(4 / If[cp, parts, d] * i, 1.1), (4 / If[cp, parts, d] * i, 1.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD5Partitions
  52. Sequence(Segment[(6 + 4 / If[cp, parts, b] * i, 6.1), (6 + 4 / If[cp, parts, b] * i, 6.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB6Partitions
  53. Sequence(Segment[(6 + 4 / If[cp, parts, b] * i, 5.1), (6 + 4 / If[cp, parts, b] * i, 5.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB8Partitions
  54. Sequence(Segment[(6 + 4 / If[cp, parts, b] * i, 4.1), (6 + 4 / If[cp, parts, b] * i, 4.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB10Partitions
  55. Sequence(Segment[(6 + 4 / If[cp, parts, d] * i, 1.1), (6 + 4 / If[cp, parts, d] * i, 1.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD6Partitions
  56. Sequence(Segment[(6 + 4 / If[cp, parts, d] * i, 0.1), (6 + 4 / If[cp, parts, d] * i, 0.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD8Partitions
  57. Sequence(Segment[(6 + 4 / If[cp, parts, d] * i, -0.1), (6 + 4 / If[cp, parts, d] * i, -0.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD10Partitions
  58. Sequence(Segment[(4 / If[cp, parts, d] * i, 0.1), (4 / If[cp, parts, d] * i, 0.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD7Partitions
  59. Sequence(Segment[(4 / If[cp, parts, d] * i, -0.1), (4 / If[cp, parts, d] * i, -0.9)], i, 1, If[cp, parts, d] - 1) → FracStripCD9Partitions
  60. Sequence(Segment[(4 / If[cp, parts, b] * i, 5.1), (4 / If[cp, parts, b] * i, 5.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB7Partitions
  61. Sequence(Segment[(4 / If[cp, parts, b] * i, 4.1), (4 / If[cp, parts, b] * i, 4.9)], i, 1, If[cp, parts, b] - 1) → FracStripAB9Partitions
  62. Segment((12.192632439999999, 0.47543172), (16.732632440000003, 0.47543172)) → SumLine
  63. Segment((12.665158779999999, 2.6284661199999997), (12.64515878, 1.46846612)) → AddSignVert
  64. Segment((12.116438780000001, 2.06389612), (13.23643878, 2.06389612)) → AddSignHoriz