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P.3 使用秤称量物体（英文版）

P.3 使用秤称量物体（英文版）
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2020-05-22 19:02
圆多边形角数列滑块动画
① 该范例通过交互式秤盘模拟，演示如何称量物体并读取重量，帮助学生理解质量与称量的基本概念。② 核心数学概念包括数字比较、单位认识（如克/千克）以及简单的算术运算（如加减法），同时涉及随机数生成和几何图形（圆、多边形）的视觉呈现。③ 作图要点：从构造摘要可见，使用了Circle、Point、Sequence、Polygon、Segment、Vector、Textfield、Angle、Random等GeoGebra命令，创建了秤盘、指针、刻度、随机物体及文本输入框，通过滑块或随机数控制物体重量，实现动态称量过程。④ 适合小学低年级（如P.3，即三年级）数学教学，用于认识秤、练习读数、比较轻重，也可作为双语教学资源。

GeoGebra 命令及参数

  1. Circle(E, 3.2) → e
  2. Point(e) → F
  3. Sequence(Rotate[F, (9 * a°), E], a, 0, 39) → list_{17}
  4. Sequence(Rotate[F, (45 * a°), E], a, 0, 7) → list_{11}
  5. Sequence(Rotate[F, (18 * a°), E], a, 0, 19) → list_5
  6. Polygon(A, B, D, C) → q1, a, b, d, c
  7. Segment(F, F_{1}) → f
  8. Sequence(Segment[Rotate[F, (90 * a°), E], Rotate[F_{1}, (90 * a°), E]], a, 0, 3) → list_1
  9. Segment(F, F_{2}) → f_3
  10. Sequence(Sequence[Segment[Rotate[F, (90 * a°) + (18 * b°), E], Rotate[F_{2}, (90 * a°) + (18 * b°), E]], b, 1, 4], a, 0, 3) → list_2
  11. Segment(Z_{list10-1}, Z_{list10-3}) → z_{1}
  12. Segment(Z_{list10-6}, Z_{list10-4}) → w_{1}
  13. Segment(Z_{list10-3}, Z_{list10-6}) → wz_{1}
  14. Circle(G, 1) → g
  15. Point(g) → H
  16. Segment(H, H_{1}) → h
  17. Sequence(Segment[Rotate[H, (90 * a°), G], Rotate[H_{1}, (90 * a°), G]], a, 0, 3) → list_4
  18. Circle(E, 3.2) → e_{1}
  19. Polygon(I, I', I''', I'') → q2, i, i', i''', i''
  20. Polygon(J, J', J''', J'') → q3, j, j', j''', j''
  21. Polygon(K, K', K''', K'') → q4, k, k', k''', k''
  22. Vector(E, F) → u
  23. Point(list_5) → F_{list5}
  24. Vector(E, F_{list5}) → v_{list5}
  25. Polygon(Z_{list10-2}, Z_{list10-5}, Z_{list10-4}, Z_{list10-1}) → q5, z', w', w_2, z_2
  26. Polygon(Z_{list10-2}, Z_{list10-5}, Z_{list10-4}, Z_{list10-1}) → q6, z'_1, w'_1, w_3, z_3
  27. Polygon(Z_{list1-1}, Z_{list1-2}, Z_{list1-4}, Z_{list1-3}) → q7, z_{list1-1}, z_{list1-2}, z_{list1-4}, z_{list1-3}
  28. Sequence(Segment[Rotate[F, (72 * a°), E], Rotate[F_{1}, (72 * a°), E]], a, 0, 4) → list_{6}
  29. Segment(Z_{list2-1}, Z_{list2-3}) → l
  30. Segment(Z_{list2-2}, Z_{list2-4}) → m
  31. Segment(Z_{list2-3}, Z_{list2-4}) → n
  32. Polygon(Z_{list2-1}, Z_{list2-2}, Z_{list2-6}, Z_{list2-5}) → q8, w_{list2-1}, w_{list2-2}, w_{list2-6}, w_{list2-5}
  33. Circle(N, 1) → p
  34. Segment(N', N'') → q
  35. Sequence(Segment[Rotate[N', (72 * a°), N], Rotate[N'', (72 * a°), N]], a, 0, 4) → list_7
  36. Polygon(Z_{list6-1}, Z_{list6-2}, Z_{list6-3}, Z_{list6-4}) → q9, z_{list6-1}, z_{list6-2}, z_{list6-3}, z_{list6-4}
  37. Sequence(Segment[Rotate[F, (36 * a°), E], Rotate[F_{1}, (36 * a°), E]], a, 0, 9) → list_8
  38. Circle(O, 1) → r
  39. Segment(O', O'') → s
  40. Sequence(Segment[Rotate[O', (36 * a°), O], Rotate[O'', (36 * a°), O]], a, 0, 9) → list_9
  41. Polygon(Z_{list8-1}, Z_{list8-2}, Z_{list8-4}, Z_{list8-3}) → q10, z_{list8-1}, z_{list8-2}, z_{list8-4}, z_{list8-3}
  42. Sequence(Sequence[Segment[Rotate[F, (90 * a°) + (45 * b°), E], Rotate[F_{2}, (90 * a°) + (45 * b°), E]], b, 1, 1], a, 0, 3) → list_{10}
  43. Point(list_{11}) → F_{list11}
  44. Vector(E, F_{list11}) → v_{list11}
  45. Segment(Z_{list10-7}, Z_{list10-8}) → t
  46. Sequence(Sequence[Segment[Rotate[F, (72 * a°) + (36 * b°), E], Rotate[F_{2}, (72 * a°) + (36 * b°), E]], b, 1, 1], a, 0, 4) → list_{12}
  47. Sequence(Rotate[F, (36 * a°), E], a, 0, 9) → list_{13}
  48. Point(list_{13}) → F_{list13}
  49. Vector(E, F_{list13}) → v_{list13}
  50. Sequence(Sequence[Segment[Rotate[F, (90 * a°) + (9 * b°), E], Rotate[F_{2}, (90 * a°) + (9 * b°), E]], b, 1, 9], a, 0, 3) → list_{14}
  51. Segment(F, F_{3}) → f_{2}
  52. Sequence(Sequence[Segment[Rotate[F, (90 * a°) + (45 * b°), E], Rotate[F_{3}, (90 * a°) + (45 * b°), E]], b, 1, 1], a, 0, 3) → list_{15}
  53. Segment(Z_{list14-2}, Z_{list14-1}) → f_1
  54. Segment(Z_{list14-4}, Z_{list14-3}) → g_1
  55. Segment(Z_{list14-1}, Z_{list14-3}) → h_1
  56. Sequence(Segment[(a, -3), (a, -2.6)], a, 14 + 2 / 10, 16 - 2 / 10, 2 / 10) → list_{16}
  57. Segment(Z_{list14-5}, Z_{list14-6}) → i_1
  58. Point(list_{17}) → F_{list17}
  59. Sequence(Segment[(a, -3), (a, -2.5)], a, 11 + 2 / 5, 13 - 2 / 5, 2 / 5) → list_3
  60. Vector(E, F_{list17}) → v_{list17}
  61. Polygon(Z_{list14-2}, Z_{list14-4}, Z_{list14-8}, Z_{list14-7}) → q11, z_{list14-2}, z_{list14-4}, z_{list14-8}, z_{list14-7}
  62. Sequence(Sequence[Segment[Rotate[F, (72 * a°) + (14.4 * b°), E], Rotate[F_{2}, (72 * a°) + (14.4 * b°), E]], b, 1, 4], a, 0, 4) → list_{18}
  63. Sequence(Rotate[F, (14.4 * a°), E], a, 0, 24) → list_{19}
  64. Point(list_{19}) → F_{list19}
  65. Vector(E, F_{list19}) → v_{list19}
  66. Sequence(Sequence[Segment[Rotate[F, (72 * a°) + (7.2 * b°), E], Rotate[F_{2}, (72 * a°) + (7.2 * b°), E]], b, 1, 9], a, 0, 4) → list_{20}
  67. Sequence(Rotate[F, (7.2 * a°), E], a, 0, 49) → list_{21}
  68. Point(list_{21}) → F_{list21}
  69. Vector(E, F_{list21}) → v_{list21}
  70. Sequence(Sequence[Segment[Rotate[F, (72 * a°) + (36 * b°), E], Rotate[F_{3}, (72 * a°) + (36 * b°), E]], b, 1, 1], a, 0, 4) → list_{22}
  71. Sequence(Sequence[Segment[Rotate[F, (36 * a°) + (18 * b°), E], Rotate[F_{2}, (36 * a°) + (18 * b°), E]], b, 1, 1], a, 0, 9) → list_{23}
  72. Sequence(Rotate[F, (18 * a°), E], a, 0, 19) → list_{24}
  73. Point(list_{24}) → F_{list24}
  74. Vector(E, F_{list24}) → v_{list24}
  75. Sequence(Sequence[Segment[Rotate[F, (36 * a°) + (7.2 * b°), E], Rotate[F_{2}, (36 * a°) + (7.2 * b°), E]], b, 1, 4], a, 0, 9) → list_{25}
  76. Sequence(Rotate[F, (7.2 * a°), E], a, 0, 49) → list_{26}
  77. Point(list_{26}) → F_{list26}
  78. Vector(E, F_{list26}) → v_{list26}
  79. Sequence(Sequence[Segment[Rotate[F, (36 * a°) + (3.6 * b°), E], Rotate[F_{2}, (36 * a°) + (3.6 * b°), E]], b, 1, 9], a, 0, 9) → list_{27}
  80. Sequence(Sequence[Segment[Rotate[F, (36 * a°) + (18 * b°), E], Rotate[F_{3}, (36 * a°) + (18 * b°), E]], b, 1, 1], a, 0, 9) → list_{28}
  81. Sequence(Rotate[F, (3.6 * a°), E], a, 0, 99) → list_{29}
  82. Point(list_{29}) → F_{list29}
  83. Vector(E, F_{list29}) → v_{list29}
  84. Textfield(ans_{1}) → inputBox1
  85. Textfield(ans_{2}) → inputBox2
  86. Textfield(ans_{3}) → inputBox3
  87. Textfield(ans_{4}) → inputBox4
  88. Angle(F_{list11}, E, F) → α_{list11}
  89. Angle(F_{list5}, E, F) → α_{list5}
  90. Angle(F_{list17}, E, F) → α_{list17}
  91. Angle(F_{list13}, E, F) → α_{list13}
  92. Angle(F_{list19}, E, F) → α_{list19}
  93. Angle(F_{list21}, E, F) → α_{list21}
  94. Angle(F_{list24}, E, F) → α_{list24}
  95. Angle(F_{list26}, E, F) → α_{list26}
  96. Angle(F_{list29}, E, F) → α_{list29}
  97. Random(1, 99) → r_{l}
  98. Random(1, 99) → r_{s}
  99. Random(1, 100) → r_{kg}
  100. Polygon(P, Q, R, S) → q12, p_1, q_1, r_1, s_1

AI 绘图提示语参考

绘制一个模拟称重秤的交互图形：中央是一个圆形表盘，表盘上有均匀的刻度线，包括较长的主刻度和较短的次刻度，以及一个可旋转的指针。表盘下方连接一个多边形秤盘，秤盘上放置随机形状的物体（如多边形或圆形）。表盘周围有多个小圆，每个小圆内带有放射状刻度线，表示不同的砝码或重量选项。整体布局对称，包含多个几何元素，用于演示称重和读数过程。
以上提示语为根据原始绘图命令整理而来，仅供参考。