积极 AI Logo 积极 AI

有理数大小比较——分数在数轴上的表示

有理数大小比较——分数在数轴上的表示
几何画板及绘图内容加载中，请稍等……
2020-08-18 22:15
解析几何不等式几何作图函数图像
本范例演示在数轴上比较两个有理数（分数）的大小关系，通过动态点与数轴标记直观展示分数大小的判断过程。核心数学概念包括有理数、分数、同分母与异分母比较、数轴表示以及大小关系（大于、小于、等于）。作图要点涉及 GeoGebra 命令 Min、Max、If、Segment、Polygon、Text、Point，并使用 Point、Segment、Polygon、Text 等对象构建数轴、分数标记点及关系选择框，其中 NumLnFrac1、NumLnFrac2 等对象用于表示数轴上的分数位置，relationshipChoices 用于交互式选择大小关系。适合初中阶段有理数教学，也可用于小学高年级分数大小比较的课堂演示与学生自主探究。

GeoGebra 命令及参数

  1. Min(c_1, d) → c
  2. Max(Sequence[If[Mod[c, i] + Mod[d, i] ≟ 0, i, -1], i, 1, Min[{c, d}]]) → factor_2
  3. If(factor_2 > 0, factor_2, 1) → factor_4
  4. Min(a_1, b) → a
  5. Max(Sequence[If[Mod[a, i] + Mod[b, i] ≟ 0, i, -1], i, 1, Min[{a, b}]]) → factor_1
  6. If(factor_1 > 0, factor_1, b) → factor_3
  7. Max(Sequence[If[Mod[l, i] + Mod[n, i] ≟ 0, i, -1], i, 1, Min[{l, n}]]) → factor
  8. Segment(C, D) → e
  9. Segment((x(C) + (1 / 8 * (x(D) - x(C))), y(C) + 0.1), (x(C) + (1 / 8 * (x(D) - x(C))), y(C) - 0.1)) → g
  10. Segment((x(C) + (0 / 8 * (x(D) - x(C))), y(C) + 0.2), (x(C) + (0 / 8 * (x(D) - x(C))), y(C) - 0.2)) → f
  11. Segment((x(C) + (2 / 8 * (x(D) - x(C))), y(C) + 0.2), (x(C) + (2 / 8 * (x(D) - x(C))), y(C) - 0.2)) → h
  12. Segment((x(C) + (3 / 8 * (x(D) - x(C))), y(C) + 0.1), (x(C) + (3 / 8 * (x(D) - x(C))), y(C) - 0.1)) → i
  13. Segment((x(C) + (4 / 8 * (x(D) - x(C))), y(C) + 0.2), (x(C) + (4 / 8 * (x(D) - x(C))), y(C) - 0.2)) → j
  14. Segment((x(C) + (5 / 8 * (x(D) - x(C))), y(C) + 0.1), (x(C) + (5 / 8 * (x(D) - x(C))), y(C) - 0.1)) → p
  15. Segment((x(C) + (6 / 8 * (x(D) - x(C))), y(C) + 0.2), (x(C) + (6 / 8 * (x(D) - x(C))), y(C) - 0.2)) → q
  16. Segment((x(C) + (7 / 8 * (x(D) - x(C))), y(C) + 0.1), (x(C) + (7 / 8 * (x(D) - x(C))), y(C) - 0.1)) → r
  17. Segment((x(C) + (8 / 8 * (x(D) - x(C))), y(C) + 0.2), (x(C) + (8 / 8 * (x(D) - x(C))), y(C) - 0.2)) → s
  18. Polygon(G, H, I, J) → poly1, g_1, h_1, i_1, j_1
  19. Segment(H, I) → t
  20. Segment(G, H) → b_1
  21. Segment(I, J) → d_1
  22. Segment(J, G) → e_1
  23. Polygon(G, (x(G) + (a / b * (x(H) - x(G))), y(G)), (x(J) + (a / b * (x(H) - x(G))), y(J)), J) → poly2, g_2, f_1, k_1, j_2
  24. Segment((x(G) + (1 / b * (x(H) - x(G))), y(G)), (x(G) + (1 / b * (x(H) - x(G))), y(G) - 1)) → l_1
  25. Segment((x(G) + (2 / b * (x(H) - x(G))), y(G)), (x(G) + (2 / b * (x(H) - x(G))), y(G) - 1)) → m_1
  26. Segment((x(G) + (3 / b * (x(H) - x(G))), y(G)), (x(G) + (3 / b * (x(H) - x(G))), y(G) - 1)) → n_1
  27. Segment((x(G) + (4 / b * (x(H) - x(G))), y(G)), (x(G) + (4 / b * (x(H) - x(G))), y(G) - 1)) → p_1
  28. Segment((x(G) + (5 / b * (x(H) - x(G))), y(G)), (x(G) + (5 / b * (x(H) - x(G))), y(G) - 1)) → q_1
  29. Segment((x(G) + (6 / b * (x(H) - x(G))), y(G)), (x(G) + (6 / b * (x(H) - x(G))), y(G) - 1)) → r_1
  30. Segment((x(G) + (7 / b * (x(H) - x(G))), y(G)), (x(G) + (7 / b * (x(H) - x(G))), y(G) - 1)) → s_1
  31. Segment((x(G) + (8 / b * (x(H) - x(G))), y(G)), (x(G) + (8 / b * (x(H) - x(G))), y(G) - 1)) → t_1
  32. Segment((x(G) + (9 / b * (x(H) - x(G))), y(G)), (x(G) + (9 / b * (x(H) - x(G))), y(G) - 1)) → a_2
  33. Segment((x(G) + (10 / b * (x(H) - x(G))), y(G)), (x(G) + (10 / b * (x(H) - x(G))), y(G) - 1)) → b_2
  34. Segment((x(G) + (11 / b * (x(H) - x(G))), y(G)), (x(G) + (11 / b * (x(H) - x(G))), y(G) - 1)) → c_2
  35. Polygon(K, L, M, N) → poly3, k_2, l_2, m_2, n_2
  36. Polygon(K, (x(K) + (c / d * (x(L) - x(K))), y(K)), (x(K) + (c / d * (x(L) - x(K))), y(M)), N) → poly4, k_3, d_2, e_2, n_3
  37. Segment((x(K) + (1 / d * (x(L) - x(K))), y(K)), (x(K) + (1 / d * (x(L) - x(K))), y(K) - 1)) → f_2
  38. Segment((x(K) + (2 / d * (x(L) - x(K))), y(K)), (x(K) + (2 / d * (x(L) - x(K))), y(K) - 1)) → h_2
  39. Segment((x(K) + (3 / d * (x(L) - x(K))), y(K)), (x(K) + (3 / d * (x(L) - x(K))), y(K) - 1)) → i_2
  40. Segment((x(K) + (4 / d * (x(L) - x(K))), y(K)), (x(K) + (4 / d * (x(L) - x(K))), y(K) - 1)) → p_2
  41. Segment((x(K) + (5 / d * (x(L) - x(K))), y(K)), (x(K) + (5 / d * (x(L) - x(K))), y(K) - 1)) → q_2
  42. Segment((x(K) + (6 / d * (x(L) - x(K))), y(K)), (x(K) + (6 / d * (x(L) - x(K))), y(K) - 1)) → r_2
  43. Segment((x(K) + (7 / d * (x(L) - x(K))), y(K)), (x(K) + (7 / d * (x(L) - x(K))), y(K) - 1)) → s_2
  44. Segment((x(K) + (8 / d * (x(L) - x(K))), y(K)), (x(K) + (8 / d * (x(L) - x(K))), y(K) - 1)) → t_2
  45. Segment((x(K) + (9 / d * (x(L) - x(K))), y(K)), (x(K) + (9 / d * (x(L) - x(K))), y(K) - 1)) → a_3
  46. Segment((x(K) + (10 / d * (x(L) - x(K))), y(K)), (x(K) + (10 / d * (x(L) - x(K))), y(K) - 1)) → b_3
  47. Segment((x(K) + (11 / d * (x(L) - x(K))), y(K)), (x(K) + (11 / d * (x(L) - x(K))), y(K) - 1)) → c_3
  48. Polygon(BoxPt, BoxPt + (9, 0), BoxPt + (9, If[ans ∧ words, -4, -3]), BoxPt + (0, If[ans ∧ words, -4, -3])) → box, d_3, e_3, f_3, g_3
  49. If(c > 9 ∨ d > 9, "_______", "____") → frac2Vinculum
  50. If(a > 9 ∨ b > 9, "_______", "____") → frac1Vinculum
  51. Text(If[a / b > c / d, ">", If[a / b < c / d, "<", "="]]) → relationshipSymbol
  52. Text(common_1) → equivFrac1Num
  53. Text(common_2) → equivFrac2Num
  54. Text(common_3) → equivFrac1Denom
  55. Text(common_3) → equivFrac2Denom
  56. Segment(BoxPt + (0.25, -2.5), BoxPt + (8.75, -2.5)) → relationshipWordsDivider
  57. Polygon(Corner[equivFrac1Denom, 1] + (-0.1, 0.1), Corner[equivFrac1Denom, 2] + (0.1, 0.1), (x(Corner[equivFrac1Denom, 2]) + 0.1, y(Corner[equivFrac1Num, 3])), (x(Corner[equivFrac1Denom, 1]) - 0.1, y(Corner[equivFrac1Num, 4]))) → equivFrac1Box, h_3, i_3, j_3, l_3
  58. Polygon(Corner[equivFrac2Denom, 1] + (-0.1, 0.1), Corner[equivFrac2Denom, 2] + (0.1, 0.1), (x(Corner[equivFrac2Denom, 2]) + 0.1, y(Corner[equivFrac2Num, 3])), (x(Corner[equivFrac2Denom, 1]) - 0.1, y(Corner[equivFrac2Num, 4]))) → equivFrac2Box, m_3, p_3, q_3, r_3
  59. Text(If[common_1 > 99 ∨ common_3 > 99, "__________", If[common_1 > 9 ∨ common_3 > 9, "_______", "____"]]) → equivFrac1Vinculum
  60. Text(If[common_2 > 99 ∨ common_3 > 99, "__________", If[common_2 > 9 ∨ common_3 > 9, "_______", "____"]]) → equivFrac2Vinculum
  61. Text("or") → equivFrac1Or
  62. Text("or") → equivFrac2Or
  63. Segment(Midpoint[G, N], Midpoint[H, M]) → areaModelDragLimit
  64. Point(areaModelDragLimit) → areaModelDragPt
  65. Segment((x(areaModelDragPt), y(N)), (x(areaModelDragPt), y(G))) → areaModelDragLine

AI 绘图提示语参考

请绘制一个数轴，上面标有分数标记。数轴上应有两个分数点，分别代表不同的分数，通过数轴位置直观比较它们的大小。标记应清晰显示分数数值，并用箭头或文本标注大于、小于、等于关系。构造时先画数轴，再在适当位置放置分数点，最后添加比较说明文字。
以上提示语为根据原始绘图命令整理而来，仅供参考。