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多种模型展示真分数

多种模型展示真分数
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2013-11-05 00:56
解析几何几何作图函数图像
所属专题 fifth grade fractions
①本范例演示如何通过多种模型（线性、数轴、集合、面积）展示和比较真分数。②涉及核心数学概念包括分数表示、数轴、集合与面积模型。③构造要点：使用Segment, Point, Circle, Sequence, Max, Min, If, Polygon, Vector, Rotate, CircleSector等GeoGebra命令和对象。④适合小学及以上数学教学，用于直观理解真分数的不同表示方法。

GeoGebra 命令及参数

  1. Segment(K_2, K_2 + (1 - num / denom, 0)) → linearModel1SegShift
  2. Point(linearModel1SegShift) → LinearModel1PtL
  3. Circle(R_1, T_1) → Circle_{model}
  4. Point(Circle[R_1, 0.105]) → C_2
  5. Sequence(If[round(flex * x(Element[list1, i]) / y(Element[list1, i])) / flex ≟ round(flex * x(L_1)) / flex, i, 0], i, 1, Length[list1]) → list2
  6. Max(list2) → match
  7. Min(9 / denom, 1) → a9
  8. Min(4 / denom, 1) → a4
  9. Min(5 / denom, 1) → a5
  10. Min(8 / denom, 1) → a8
  11. Min(7 / denom, 1) → a7
  12. Min(6 / denom, 1) → a6
  13. Min(1 / denom, 1) → a1
  14. Min(2 / denom, 1) → a2
  15. If(denom < 10, " " + denom, "" + denom) → formatd
  16. Min(3 / denom, 1) → a3
  17. Min(10 / denom, 1) → a10
  18. Point(Circle[M, 1]) → Q
  19. Point(Circle[N, 1]) → R
  20. Point(Circle[L_1, 0.02]) → U_1
  21. Point(Circle[U_1, 0.5]) → V_1
  22. Polygon(LinearModel1PtL + (0, -0.03), LinearModel1PtL + (num / denom, -0.03), LinearModel1PtL + (num / denom, 0.03), LinearModel1PtL + (0, 0.03)) → int1, a, b, c, e
  23. If(impr > 1, 1, 0) → Rect_{show}
  24. Vector(NL_c, NL_l) → u
  25. Vector(NL_c, NL_r) → v
  26. Vector(FP_t, FP) → w
  27. If(num / denom > 1, 1, 0) → Set_{show}
  28. Segment((1, 0.13), (1, 0.17)) → i_2
  29. Segment((0, 0.13), (0, 0.17)) → j_2
  30. Segment(R_1, C_2) → m_2
  31. Rotate(C_2, angle, R_1) → D_2
  32. CircleSector(R_1, C_2, D_2) → r_3
  33. Segment(R_1, D_2) → l_2
  34. Rotate(C_2, (360 / denom)°, R_1) → B_2
  35. Sequence(Segment[Rotate[C_2, (360 * i / denom)°, R_1], R_1], i, 0, denom) → Angle_{divseq}
  36. Segment(K_2, L_2) → a_2
  37. Vector((0, 0.25), (0.1, 0.25)) → image_{vector}
  38. Sequence(Translate[pic1, Vector[i * image_{vector}]], i, 0, denom - 1) → Set_{opencat}
  39. Sequence(Translate[pic2, Vector[i * image_{vector}]], i, 0, num - 1) → Set_{closedcat}
  40. Sequence(Translate[pic3, Vector[i * image_{vector}]], i, 0, denom - 1) → Set_{openstar}
  41. Sequence(Translate[pic4, Vector[i * image_{vector}]], i, 0, num - 1) → Set_{closedstar}
  42. Sequence(Segment[(0.045 + i / 11, 0.385), Point[Circle[(0.045 + i / 11, 0.59), 0]]], i, 0, denom) → Area_{rectdiv}
  43. Polygon(R_8, F_2, G_2, E_2) → rect_{red}, r_8, f_4, g_4, e_4
  44. Segment(R_8, I_2) → b_2
  45. Segment(E_2, H_2) → n_2
  46. Sequence(Segment[(0.045 + i / (3 * denom), 0.385), Point[Circle[(0.045 + i / (3 * denom), 0.59), 0]]], i, 0, denom) → Area_{rect2}
  47. Segment(E_2, M_2) → a_3
  48. Segment(J_2, R_8) → b_3
  49. Polygon(E_2, O_2, N_2, R_8) → poly1, e_5, o_2, n_3, r_4
  50. Segment(LinearModel1PtL + (0, 0.0050), LinearModel1PtR + (0, 0.0050)) → linearModel1Line
  51. Sequence(Segment[(i, 0.13), (i, 0.17)], i, 0, 1, 1 / lineHashMarks) → lineHashMarkList
  52. Sequence(Segment[(i, 0), (i, 0.05)], i, 0, 1, 1 / lineHashMarks) → linearHashMarkList
  53. Sequence(Circle[(0.05 + i, 0.3), 0.045], i, 0, (denom - 1) / 10, 0.1) → setCircleOpen
  54. Sequence(Circle[(0.05 + i, 0.3), 0.04], i, 0, (num - 1) / 10, 0.1) → setCircleShading