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物体集合的一部分

物体集合的一部分
几何画板及绘图内容加载中，请稍等……
2022-03-17 11:37
函数数列解析几何
本范例通过计算物体集合的一部分来帮助学生理解分数的概念。涉及的核心数学概念包括分数和集合。使用了DynamicCoordinates, DivisorsList, Factors, Sequence, Polygon, Element, If, Textfield等GeoGebra命令。适合小学高年级或初中低年级学生学习分数的概念和应用。

GeoGebra 命令及参数

  1. DynamicCoordinates(P0, If[x(P0) < 2, 2, If[x(P0) > 12, 12, round(x(P0))]], If[y(P0) > -1, -1, If[y(P0) < -6, -6, round(y(P0))]]) → P
  2. DivisorsList(n) → nfactors
  3. Factors(n) →
  4. DivisorsList(m) → mfactors
  5. Factors(m) →
  6. Sequence(Segment[((i * m / Element[mfactors, mdiv]), 0), ((i * m / Element[mfactors, mdiv]), (-n))], i, 1, Element[mfactors, mdiv] - 1) → l2
  7. Sequence(Segment[(0, ((-i) * n / Element[nfactors, ndiv])), (m, ((-i) * n / Element[nfactors, ndiv]))], i, 1, Element[nfactors, ndiv] - 1) → l3
  8. Polygon({(b - b, 0), (b, 0), (b, (-h)), (b - b, (-h))}) → q101
  9. Polygon({((2 * b) - b, 0), ((2 * b), 0), ((2 * b), (-h)), ((2 * b) - b, (-h))}) → q102
  10. Polygon({((3 * b) - b, 0), ((3 * b), 0), ((3 * b), (-h)), ((3 * b) - b, (-h))}) → q103
  11. Polygon({((4 * b) - b, 0), ((4 * b), 0), ((4 * b), (-h)), ((4 * b) - b, (-h))}) → q104
  12. Polygon({((5 * b) - b, 0), ((5 * b), 0), ((5 * b), (-h)), ((5 * b) - b, (-h))}) → q105
  13. Polygon({((6 * b) - b, 0), ((6 * b), 0), ((6 * b), (-h)), ((6 * b) - b, (-h))}) → q106
  14. Polygon({((7 * b) - b, 0), ((7 * b), 0), ((7 * b), (-h)), ((7 * b) - b, (-h))}) → q107
  15. Polygon({((8 * b) - b, 0), ((8 * b), 0), ((8 * b), (-h)), ((8 * b) - b, (-h))}) → q108
  16. Polygon({((9 * b) - b, 0), ((9 * b), 0), ((9 * b), (-h)), ((9 * b) - b, (-h))}) → q109
  17. Polygon({(b - b, (-h)), (b, (-h)), (b, (-2 * h)), (b - b, (-2 * h))}) → q201
  18. Polygon({((2 * b) - b, (-h)), ((2 * b), (-h)), ((2 * b), (-2 * h)), ((2 * b) - b, (-2 * h))}) → q202
  19. Polygon({((3 * b) - b, (-h)), ((3 * b), (-h)), ((3 * b), (-2 * h)), ((3 * b) - b, (-2 * h))}) → q203
  20. Polygon({((4 * b) - b, (-h)), ((4 * b), (-h)), ((4 * b), (-2 * h)), ((4 * b) - b, (-2 * h))}) → q204
  21. Polygon({((5 * b) - b, (-h)), ((5 * b), (-h)), ((5 * b), (-2 * h)), ((5 * b) - b, (-2 * h))}) → q205
  22. Polygon({((6 * b) - b, (-h)), ((6 * b), (-h)), ((6 * b), (-2 * h)), ((6 * b) - b, (-2 * h))}) → q206
  23. Polygon({((7 * b) - b, (-h)), ((7 * b), (-h)), ((7 * b), (-2 * h)), ((7 * b) - b, (-2 * h))}) → q207
  24. Polygon({((8 * b) - b, (-h)), ((8 * b), (-h)), ((8 * b), (-2 * h)), ((8 * b) - b, (-2 * h))}) → q208
  25. Polygon({((9 * b) - b, (-h)), ((9 * b), (-h)), ((9 * b), (-2 * h)), ((9 * b) - b, (-2 * h))}) → q209
  26. Polygon({(b - b, (-2 * h)), (b, (-2 * h)), (b, (-3 * h)), (b - b, (-3 * h))}) → q301
  27. Polygon({((2 * b) - b, (-2 * h)), ((2 * b), (-2 * h)), ((2 * b), (-3 * h)), ((2 * b) - b, (-3 * h))}) → q302
  28. Polygon({((3 * b) - b, (-2 * h)), ((3 * b), (-2 * h)), ((3 * b), (-3 * h)), ((3 * b) - b, (-3 * h))}) → q303
  29. Polygon({((4 * b) - b, (-2 * h)), ((4 * b), (-2 * h)), ((4 * b), (-3 * h)), ((4 * b) - b, (-3 * h))}) → q304
  30. Polygon({((5 * b) - b, (-2 * h)), ((5 * b), (-2 * h)), ((5 * b), (-3 * h)), ((5 * b) - b, (-3 * h))}) → q305
  31. Polygon({((6 * b) - b, (-2 * h)), ((6 * b), (-2 * h)), ((6 * b), (-3 * h)), ((6 * b) - b, (-3 * h))}) → q306
  32. Polygon({((7 * b) - b, (-2 * h)), ((7 * b), (-2 * h)), ((7 * b), (-3 * h)), ((7 * b) - b, (-3 * h))}) → q307
  33. Polygon({((8 * b) - b, (-2 * h)), ((8 * b), (-2 * h)), ((8 * b), (-3 * h)), ((8 * b) - b, (-3 * h))}) → q308
  34. Polygon({((9 * b) - b, (-2 * h)), ((9 * b), (-2 * h)), ((9 * b), (-3 * h)), ((9 * b) - b, (-3 * h))}) → q309
  35. Polygon({(b - b, (-3 * h)), (b, (-3 * h)), (b, (-4 * h)), (b - b, (-4 * h))}) → q401
  36. Polygon({((2 * b) - b, (-3 * h)), ((2 * b), (-3 * h)), ((2 * b), (-4 * h)), ((2 * b) - b, (-4 * h))}) → q402
  37. Polygon({((3 * b) - b, (-3 * h)), ((3 * b), (-3 * h)), ((3 * b), (-4 * h)), ((3 * b) - b, (-4 * h))}) → q403
  38. Polygon({((4 * b) - b, (-3 * h)), ((4 * b), (-3 * h)), ((4 * b), (-4 * h)), ((4 * b) - b, (-4 * h))}) → q404
  39. Polygon({((5 * b) - b, (-3 * h)), ((5 * b), (-3 * h)), ((5 * b), (-4 * h)), ((5 * b) - b, (-4 * h))}) → q405
  40. Polygon({((6 * b) - b, (-3 * h)), ((6 * b), (-3 * h)), ((6 * b), (-4 * h)), ((6 * b) - b, (-4 * h))}) → q406
  41. Polygon({((7 * b) - b, (-3 * h)), ((7 * b), (-3 * h)), ((7 * b), (-4 * h)), ((7 * b) - b, (-4 * h))}) → q407
  42. Polygon({((8 * b) - b, (-3 * h)), ((8 * b), (-3 * h)), ((8 * b), (-4 * h)), ((8 * b) - b, (-4 * h))}) → q408
  43. Polygon({((9 * b) - b, (-3 * h)), ((9 * b), (-3 * h)), ((9 * b), (-4 * h)), ((9 * b) - b, (-4 * h))}) → q409
  44. Polygon({(b - b, (-4 * h)), (b, (-4 * h)), (b, (-5 * h)), (b - b, (-5 * h))}) → q501
  45. Polygon({((2 * b) - b, (-4 * h)), ((2 * b), (-4 * h)), ((2 * b), (-5 * h)), ((2 * b) - b, (-5 * h))}) → q502
  46. Polygon({((3 * b) - b, (-4 * h)), ((3 * b), (-4 * h)), ((3 * b), (-5 * h)), ((3 * b) - b, (-5 * h))}) → q503
  47. Polygon({((4 * b) - b, (-4 * h)), ((4 * b), (-4 * h)), ((4 * b), (-5 * h)), ((4 * b) - b, (-5 * h))}) → q504
  48. Polygon({((5 * b) - b, (-4 * h)), ((5 * b), (-4 * h)), ((5 * b), (-5 * h)), ((5 * b) - b, (-5 * h))}) → q505
  49. Polygon({((6 * b) - b, (-4 * h)), ((6 * b), (-4 * h)), ((6 * b), (-5 * h)), ((6 * b) - b, (-5 * h))}) → q506
  50. Polygon({((7 * b) - b, (-4 * h)), ((7 * b), (-4 * h)), ((7 * b), (-5 * h)), ((7 * b) - b, (-5 * h))}) → q507
  51. Polygon({((8 * b) - b, (-4 * h)), ((8 * b), (-4 * h)), ((8 * b), (-5 * h)), ((8 * b) - b, (-5 * h))}) → q508
  52. Polygon({((9 * b) - b, (-4 * h)), ((9 * b), (-4 * h)), ((9 * b), (-5 * h)), ((9 * b) - b, (-5 * h))}) → q509
  53. Polygon({(b - b, (-5 * h)), (b, (-5 * h)), (b, (-6 * h)), (b - b, (-6 * h))}) → q601
  54. Polygon({((2 * b) - b, (-5 * h)), ((2 * b), (-5 * h)), ((2 * b), (-6 * h)), ((2 * b) - b, (-6 * h))}) → q602
  55. Polygon({((3 * b) - b, (-5 * h)), ((3 * b), (-5 * h)), ((3 * b), (-6 * h)), ((3 * b) - b, (-6 * h))}) → q603
  56. Polygon({((4 * b) - b, (-5 * h)), ((4 * b), (-5 * h)), ((4 * b), (-6 * h)), ((4 * b) - b, (-6 * h))}) → q604
  57. Polygon({((5 * b) - b, (-5 * h)), ((5 * b), (-5 * h)), ((5 * b), (-6 * h)), ((5 * b) - b, (-6 * h))}) → q605
  58. Polygon({((6 * b) - b, (-5 * h)), ((6 * b), (-5 * h)), ((6 * b), (-6 * h)), ((6 * b) - b, (-6 * h))}) → q606
  59. Polygon({((7 * b) - b, (-5 * h)), ((7 * b), (-5 * h)), ((7 * b), (-6 * h)), ((7 * b) - b, (-6 * h))}) → q607
  60. Polygon({((8 * b) - b, (-5 * h)), ((8 * b), (-5 * h)), ((8 * b), (-6 * h)), ((8 * b) - b, (-6 * h))}) → q608
  61. Polygon({((9 * b) - b, (-5 * h)), ((9 * b), (-5 * h)), ((9 * b), (-6 * h)), ((9 * b) - b, (-6 * h))}) → q609
  62. Polygon({((10 * b) - b, 0), ((10 * b), 0), ((10 * b), (-h)), ((10 * b) - b, (-h))}) → q110
  63. Polygon({((11 * b) - b, 0), ((11 * b), 0), ((11 * b), (-h)), ((11 * b) - b, (-h))}) → q111
  64. Polygon({((12 * b) - b, 0), ((12 * b), 0), ((12 * b), (-h)), ((12 * b) - b, (-h))}) → q112
  65. Polygon({((10 * b) - b, (-h)), ((10 * b), (-h)), ((10 * b), (-2 * h)), ((10 * b) - b, (-2 * h))}) → q210
  66. Polygon({((11 * b) - b, (-h)), ((11 * b), (-h)), ((11 * b), (-2 * h)), ((11 * b) - b, (-2 * h))}) → q211
  67. Polygon({((12 * b) - b, (-h)), ((12 * b), (-h)), ((12 * b), (-2 * h)), ((12 * b) - b, (-2 * h))}) → q212
  68. Polygon({((10 * b) - b, (-2 * h)), ((10 * b), (-2 * h)), ((10 * b), (-3 * h)), ((10 * b) - b, (-3 * h))}) → q310
  69. Polygon({((11 * b) - b, (-2 * h)), ((11 * b), (-2 * h)), ((11 * b), (-3 * h)), ((11 * b) - b, (-3 * h))}) → q311
  70. Polygon({((12 * b) - b, (-2 * h)), ((12 * b), (-2 * h)), ((12 * b), (-3 * h)), ((12 * b) - b, (-3 * h))}) → q312
  71. Polygon({((10 * b) - b, (-3 * h)), ((10 * b), (-3 * h)), ((10 * b), (-4 * h)), ((10 * b) - b, (-4 * h))}) → q410
  72. Polygon({((11 * b) - b, (-3 * h)), ((11 * b), (-3 * h)), ((11 * b), (-4 * h)), ((11 * b) - b, (-4 * h))}) → q411
  73. Polygon({((12 * b) - b, (-3 * h)), ((12 * b), (-3 * h)), ((12 * b), (-4 * h)), ((12 * b) - b, (-4 * h))}) → q412
  74. Polygon({((10 * b) - b, (-4 * h)), ((10 * b), (-4 * h)), ((10 * b), (-5 * h)), ((10 * b) - b, (-5 * h))}) → q510
  75. Polygon({((11 * b) - b, (-4 * h)), ((11 * b), (-4 * h)), ((11 * b), (-5 * h)), ((11 * b) - b, (-5 * h))}) → q511
  76. Polygon({((12 * b) - b, (-4 * h)), ((12 * b), (-4 * h)), ((12 * b), (-5 * h)), ((12 * b) - b, (-5 * h))}) → q512
  77. Polygon({((10 * b) - b, (-5 * h)), ((10 * b), (-5 * h)), ((10 * b), (-6 * h)), ((10 * b) - b, (-6 * h))}) → q610
  78. Polygon({((11 * b) - b, (-5 * h)), ((11 * b), (-5 * h)), ((11 * b), (-6 * h)), ((11 * b) - b, (-6 * h))}) → q611
  79. Polygon({((12 * b) - b, (-5 * h)), ((12 * b), (-5 * h)), ((12 * b), (-6 * h)), ((12 * b) - b, (-6 * h))}) → q612
  80. Element(mfactors, mdiv) → numcolumns
  81. Element(nfactors, ndiv) → numrows
  82. Polygon({(0, 0), (x(P), 0), P, (0, y(P))}) → q1
  83. If(response1 ≟ "", false, true) → input1
  84. If(response2 ≟ "", false, true) → input2
  85. If(response1 ≟ ans1, true, false) → correct1
  86. If(response2 ≟ ans2, true, false) → correct2
  87. Textfield(response2) → InputBox2
  88. Textfield(response1) → InputBox1
  89. DynamicCoordinates(P0_{1}, If[x(P0_{1}) < 2, 2, If[x(P0_{1}) > 12, 12, round(x(P0_{1}))]], If[y(P0_{1}) > -1, -1, If[y(P0_{1}) < -6, -6, round(y(P0_{1}))]]) → P_{1}
  90. DivisorsList(n_{1}) → nfactors_{1}
  91. Factors(n_{1}) →
  92. DivisorsList(m_{1}) → mfactors_{1}
  93. Factors(m_{1}) →
  94. Sequence(Translate[pic1, (i - 1, -1)], i, 1, m) → l1
  95. Sequence(Translate[l1, (0, (-j) + 1)], j, 1, n) → m1

AI 绘图提示语参考

画一个坐标系，原点附近有一个动态点，其横纵坐标分别限制在2到12和-1到-6之间。基于一个数字n，画出其所有因数构成的序列，每个因数对应一个水平线段，从x轴上对应位置向下延伸。基于另一个数字m，画出其所有因数构成的序列，每个因数对应一个垂直线段，从y轴上对应位置向右延伸。在x轴上，从b到9b的位置，依次画出10个矩形，每个矩形高度为h。在y轴下方，从-2h到-5h的位置，依次画出10个矩形，每个矩形宽度为b。所有矩形都平行于x轴或y轴。
以上提示语为根据原始绘图命令整理而来，仅供参考。