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比较有理数 – 分数

比较有理数 – 分数
几何画板及绘图内容加载中，请稍等……
2020-08-18 22:15
不等式几何作图函数图像
这个GeoGebra范例通过动态图形直观演示有理数与分数的大小比较过程，帮助学生理解分数在数轴上的相对位置及其不等关系。核心数学概念包括有理数、分数比较、不等式原理以及数轴表示。作图要点上，使用了Min和Max命令设定数值范围，If命令实现条件判断逻辑，Segment和Polygon命令绘制数轴与分数条等几何元素，Text命令添加数值标签，Point命令定义关键点位。对象如NumLnFrac1和NumLnFrac2用于表示两个分数的数轴位置，factor系列变量控制分数值的调整。该范例适合初中数学教学场景，可用于分数比较的直观教学与互动练习。

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

绘制一条水平数轴，两端标记刻度，并在数轴上方放置两个矩形条，分别代表两个分数。每个矩形条被等分为若干小格，其中一部分格子被填充颜色，表示分数的分子部分。两个矩形条下方各有一条垂直线段，用于对齐数轴上的对应位置。数轴上的刻度线长短交替，以显示分数在数轴上的相对位置。整体布局清晰，便于比较两个分数的大小关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。