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利用视觉模式推导线性方程：通过观察规律建立代数关系

利用视觉模式推导线性方程：通过观察规律建立代数关系
几何画板及绘图内容加载中，请稍等……
2023-02-24 03:36
函数数列解析几何
这个范例通过观察视觉模式中的数字变化规律，帮助学生理解线性方程的建立方法。核心数学概念包括变量关系、规律预测和方程建模。作图要点涉及使用GeoGebra命令如Shuffle、Element和Sequence来动态展示模式变化。适合6-8年级学生用于代数学习，适用于课堂练习和在线教育平台。

GeoGebra 命令及参数

  1. Shuffle(Sequence[20]) → randomList1, {12, 9, 18, 11, 20, 13, 2, 17, 6, 8, 3, 16, 1, 10, 14, 5, 19, 7, 15, 4}
  2. Shuffle(Sequence[600]) → randomVars, {193, 71, 77, 538, 315, 505, 39, 594, 526, 352, 567, 591, 79, 406, 181, 2, 137, 127, 587, 508, 551, 477, 503, 416, 301, 343, 145, 355, 203, 174, 98, 501, 92, 208, 271, 560, 380, 201, 97, 197, 185, 223, 555, 568, 392, 37, 212, 452, 229, 431, 192, 577, 350, 252, 529, 489, 221, 160, 110, 78, 51, 217, 143, 289, 543, 398, 348, 236, 142, 595, 55, 243, 48, 16, 100, 453, 62, 257, 469, 169, 285, 418, 286, 230, 549, 163, 272, 509, 19, 419, 214, 308, 118, 234, 313, 411, 495, 553, 471, 305, 134, 578, 278, 128, 327, 72, 309, 338, 476, 190, 432, 346, 173, 117, 46, 321, 52, 518, 164, 13, 318, 258, 381, 206, 41, 14, 237, 167, 316, 326, 21, 425, 539, 225, 180, 494, 32, 546, 297, 44, 29, 513, 107, 85, 250, 144, 437, 135, 176, 200, 162, 248, 126, 122, 113, 438, 391, 178, 149, 592, 319, 288, 90, 152, 590, 528, 159, 81, 349, 404, 207, 400, 593, 354, 25, 82, 211, 215, 384, 564, 228, 396, 80, 156, 569, 579, 66, 475, 455, 22, 5, 166, 121, 329, 199, 132, 548, 443, 525, 23, 61, 136, 109, 304, 397, 399, 148, 486, 56, 280, 468, 269, 420, 172, 267, 558, 195, 571, 182, 426, 559, 563, 550, 202, 557, 488, 410, 424, 235, 454, 146, 462, 533, 485, 395, 75, 171, 290, 30, 89, 562, 10, 187, 283, 247, 490, 393, 444, 65, 94, 293, 382, 232, 307, 362, 246, 249, 359, 255, 140, 545, 521, 456, 328, 276, 91, 361, 222, 576, 111, 554, 484, 219, 322, 516, 584, 378, 101, 556, 102, 233, 8, 439, 213, 566, 189, 99, 198, 36, 600, 435, 335, 184, 445, 216, 147, 512, 405, 541, 574, 281, 519, 158, 183, 103, 461, 436, 295, 244, 421, 358, 306, 57, 259, 50, 383, 597, 504, 54, 251, 264, 413, 351, 253, 261, 356, 403, 506, 478, 53, 112, 175, 83, 370, 386, 226, 204, 88, 367, 240, 86, 479, 31, 179, 540, 387, 268, 265, 451, 108, 442, 124, 379, 580, 20, 534, 572, 256, 522, 331, 58, 241, 487, 341, 401, 517, 76, 388, 161, 336, 3, 24, 254, 427, 245, 422, 205, 69, 238, 377, 273, 28, 242, 153, 157, 472, 371, 596, 188, 260, 275, 125, 105, 333, 570, 390, 40, 344, 120, 433, 154, 373, 1, 510, 339, 300, 209, 239, 417, 598, 15, 524, 170, 151, 412, 95, 473, 368, 582, 583, 227, 340, 523, 465, 218, 38, 317, 67, 64, 332, 194, 7, 279, 402, 483, 266, 561, 129, 287, 63, 43, 532, 325, 531, 302, 133, 589, 448, 168, 414, 507, 375, 496, 385, 499, 447, 298, 457, 123, 429, 599, 70, 130, 376, 34, 131, 530, 581, 459, 515, 407, 441, 585, 220, 320, 314, 33, 514, 311, 430, 482, 324, 323, 87, 537, 114, 4, 493, 527, 535, 365, 155, 474, 440, 342, 312, 26, 372, 296, 502, 480, 409, 586, 363, 210, 11, 497, 369, 491, 415, 449, 224, 364, 463, 330, 73, 547, 138, 141, 446, 500, 17, 60, 119, 74, 9, 49, 467, 35, 470, 481, 544, 263, 191, 360, 282, 460, 366, 434, 565, 464, 18, 262, 575, 458, 59, 291, 394, 186, 347, 511, 345, 310, 428, 374, 84, 588, 196, 47, 408, 104, 165, 150, 12, 294, 115, 466, 139, 270, 389, 96, 116, 573, 498, 299, 284, 45, 277, 450, 423, 42, 552, 292, 334, 27, 303, 353, 68, 337, 6, 177, 231, 357, 106, 492, 542, 93, 274, 536, 520}
  3. Element(randomVars, Mod[countQuestion, Length[randomVars] - 9] + 1) → startIndex
  4. Sequence(If[A ≟ 4, FIXED, Element[{FIXED, VARIABLE, EMPTY}, Mod[randomVars(startIndex + A), 2] + 1]], A, 3, 5) → patternRow2
  5. Sequence(Element[{EMPTY, VARIABLE}, Mod[randomVars(startIndex + A), 2] + 1], A, 0, 2) → patternRow1
  6. Sequence(Element[{EMPTY, VARIABLE}, Mod[randomVars(startIndex + A), 2] + 1], A, 6, 8) → patternRow3
  7. Sum(Zip[If[A ≟ FIXED, 1, 0], A, Flatten[pattern1]]) → numFixed
  8. If(patternRow2(3) ≟ FIXED, EMPTY, patternRow2(3)) → extendRight
  9. If(patternRow2(1) ≟ FIXED, EMPTY, patternRow2(1)) → extendLeft
  10. Sequence(If[A ≠ 3, Join[{{EMPTY}, If[A < 3, patternRow1, patternRow3], {EMPTY}}], Join[{{extendLeft}, patternRow2, {extendRight}}]], A, 1, 5) → pattern2
  11. Sequence(If[A ≠ 4, Join[{{EMPTY}, If[A < 4, pattern2(1), pattern2(5)], {EMPTY}}], Join[{{extendLeft}, pattern2(3), {extendRight}}]], A, 1, 7) → pattern3
  12. RemoveUndefined(Flatten[Sequence[Sequence[If[pattern3(A, B) ≠ EMPTY, Anchor3 + (B - 1, A - 1)], A, 1, 7], B, 1, 7]]) → anchorBlocks3
  13. Zip(A + (x(Anchor4 - Anchor3) + 1, 0), A, anchorBlocks3) → anchorBlocks4StartPattern
  14. Sequence(If[A ≠ 5, Join[{{EMPTY}, If[A < 5, pattern3(1), pattern3(7)], {EMPTY}}], Join[{{extendLeft}, pattern3(4), {extendRight}}]], A, 1, 9) → pattern4
  15. RemoveUndefined(Flatten[Sequence[Sequence[If[pattern4(A, B) ≠ EMPTY, Anchor4 + (B - 1, A - 1)], A, 1, 9], B, 1, 9]]) → anchorBlocks4
  16. If(patternRow2(3) ≠ EMPTY, 3, 2) → width1
  17. Flatten(Sequence[Sequence[Anchor4 + (j, i), i, 0, 8], j, 0, 8]) → patternAnchors
  18. Element(randomList1, Mod[countQuestion, 20] + 1) → randomNum1
  19. Corner(5) → layoutAppSize
  20. Element(randomVars, Mod[countQuestion, Length[randomVars]] + 1) → caseNum
  21. RemoveUndefined(Flatten[Sequence[Sequence[If[pattern1(A, B) ≟ FIXED, Anchor1 + (B - 1, A - 1)], A, 1, 3], B, 1, 3]]) → positionsX
  22. Zip(Zip[boxTool[1, 1, A], A, positionsX + (B, 0)], B, {0, x(Anchor2) - x(Anchor1) + 1, x(Anchor3) - x(Anchor1) + 2, x(Anchor4) - x(Anchor1) + 3}) → allXBlocks
  23. boxTool(1, 1, patternAnchors(E2)) → A2
  24. boxTool(1, 1, patternAnchors(E3)) → A3
  25. boxTool(1, 1, patternAnchors(E4)) → A4
  26. boxTool(1, 1, patternAnchors(E5)) → A5
  27. boxTool(1, 1, patternAnchors(E6)) → A6
  28. boxTool(1, 1, patternAnchors(E7)) → A7
  29. boxTool(1, 1, patternAnchors(E8)) → A8
  30. boxTool(1, 1, patternAnchors(E9)) → A9
  31. boxTool(1, 1, patternAnchors(E10)) → A10
  32. boxTool(1, 1, patternAnchors(E11)) → A11
  33. boxTool(1, 1, patternAnchors(E12)) → A12
  34. boxTool(1, 1, patternAnchors(E13)) → A13
  35. boxTool(1, 1, patternAnchors(E14)) → A14
  36. boxTool(1, 1, patternAnchors(E15)) → A15
  37. boxTool(1, 1, patternAnchors(E16)) → A16
  38. boxTool(1, 1, patternAnchors(E17)) → A17
  39. boxTool(1, 1, patternAnchors(E18)) → A18
  40. boxTool(1, 1, patternAnchors(E19)) → A19
  41. boxTool(1, 1, patternAnchors(E20)) → A20
  42. boxTool(1, 1, patternAnchors(E21)) → A21
  43. boxTool(1, 1, patternAnchors(E22)) → A22
  44. boxTool(1, 1, patternAnchors(E23)) → A23
  45. boxTool(1, 1, patternAnchors(E24)) → A24
  46. boxTool(1, 1, patternAnchors(E25)) → A25
  47. boxTool(1, 1, patternAnchors(E26)) → A26
  48. boxTool(1, 1, patternAnchors(E27)) → A27
  49. boxTool(1, 1, patternAnchors(E28)) → A28
  50. boxTool(1, 1, patternAnchors(E29)) → A29
  51. boxTool(1, 1, patternAnchors(E30)) → A30
  52. boxTool(1, 1, patternAnchors(E31)) → A31
  53. boxTool(1, 1, patternAnchors(E32)) → A32
  54. boxTool(1, 1, patternAnchors(E33)) → A33
  55. boxTool(1, 1, patternAnchors(E34)) → A34
  56. boxTool(1, 1, patternAnchors(E35)) → A35
  57. boxTool(1, 1, patternAnchors(E36)) → A36
  58. boxTool(1, 1, patternAnchors(E37)) → A37
  59. boxTool(1, 1, patternAnchors(E38)) → A38
  60. boxTool(1, 1, patternAnchors(E39)) → A39
  61. boxTool(1, 1, patternAnchors(E40)) → A40
  62. boxTool(1, 1, patternAnchors(E41)) → A41
  63. boxTool(1, 1, patternAnchors(E42)) → A42
  64. boxTool(1, 1, patternAnchors(E43)) → A43
  65. boxTool(1, 1, patternAnchors(E44)) → A44
  66. boxTool(1, 1, patternAnchors(E45)) → A45
  67. boxTool(1, 1, patternAnchors(E46)) → A46
  68. boxTool(1, 1, patternAnchors(E47)) → A47
  69. boxTool(1, 1, patternAnchors(E48)) → A48
  70. boxTool(1, 1, patternAnchors(E49)) → A49
  71. boxTool(1, 1, patternAnchors(E50)) → A50
  72. boxTool(1, 1, patternAnchors(E51)) → A51
  73. boxTool(1, 1, patternAnchors(E52)) → A52
  74. boxTool(1, 1, patternAnchors(E53)) → A53
  75. boxTool(1, 1, patternAnchors(E54)) → A54
  76. boxTool(1, 1, patternAnchors(E55)) → A55
  77. boxTool(1, 1, patternAnchors(E56)) → A56
  78. boxTool(1, 1, patternAnchors(E57)) → A57
  79. boxTool(1, 1, patternAnchors(E58)) → A58
  80. boxTool(1, 1, patternAnchors(E59)) → A59
  81. boxTool(1, 1, patternAnchors(E60)) → A60
  82. boxTool(1, 1, patternAnchors(E61)) → A61
  83. boxTool(1, 1, patternAnchors(E62)) → A62
  84. boxTool(1, 1, patternAnchors(E63)) → A63
  85. boxTool(1, 1, patternAnchors(E64)) → A64
  86. boxTool(1, 1, patternAnchors(E65)) → A65
  87. boxTool(1, 1, patternAnchors(E66)) → A66
  88. boxTool(1, 1, patternAnchors(E67)) → A67
  89. boxTool(1, 1, patternAnchors(E68)) → A68
  90. boxTool(1, 1, patternAnchors(E69)) → A69
  91. boxTool(1, 1, patternAnchors(E70)) → A70
  92. boxTool(1, 1, patternAnchors(E71)) → A71
  93. boxTool(1, 1, patternAnchors(E72)) → A72
  94. boxTool(1, 1, patternAnchors(E73)) → A73
  95. boxTool(1, 1, patternAnchors(E74)) → A74
  96. boxTool(1, 1, patternAnchors(E75)) → A75
  97. boxTool(1, 1, patternAnchors(E76)) → A76
  98. boxTool(1, 1, patternAnchors(E77)) → A77
  99. boxTool(1, 1, patternAnchors(E78)) → A78
  100. boxTool(1, 1, patternAnchors(E79)) → A79
  101. boxTool(1, 1, patternAnchors(E80)) → A80
  102. boxTool(1, 1, patternAnchors(E81)) → A81
  103. boxTool(1, 1, patternAnchors(E82)) → A82
  104. Zip(boxTool[1, 1, A], A, anchorBlocks4) → blocks4
  105. RemoveUndefined(Flatten[Sequence[Sequence[If[pattern1(A, B) ≠ EMPTY, Anchor1 + (B - 1, A - 1)], A, 1, 3], B, 1, 3]]) → anchorBlocks1
  106. Zip(boxTool[1, 1, A], A, anchorBlocks1) → blocks1
  107. RemoveUndefined(Flatten[Sequence[Sequence[If[pattern2(A, B) ≠ EMPTY, Anchor2 + (B - 1, A - 1)], A, 1, 5], B, 1, 5]]) → anchorBlocks2
  108. Zip(boxTool[1, 1, A], A, anchorBlocks2) → blocks2
  109. Zip(boxTool[1, 1, A], A, anchorBlocks3) → blocks3
  110. Remove(anchorBlocks4, anchorBlocks4StartPattern) → anchorsExpected
  111. Zip(boxTool[1, 1, A + (x(Anchor4 - Anchor3) + 1, 0)], A, anchorBlocks3) → fig4Hint
  112. RemoveUndefined(Sequence[If[allSelected(A), patternAnchors(A)], A, 1, Length[patternAnchors]]) → anchorsSelected
  113. Sequence((("SetValue(B" * A) * ",false)"), A, 2, 82) → cmdClearAllSelections
  114. Sum(Zip[If[A ≟ VARIABLE, 1, 0], A, Flatten[pattern1]]) → numVariable
  115. Flatten(Sequence[Sequence[pattern4(A, B) ≠ EMPTY, A, 1, 9], B, 1, 9]) → allExpectedPatternFull
  116. Take(allExpectedPatternFull, IndexOf[true, allExpectedPatternFull], Length[allExpectedPatternFull] - IndexOf[true, Reverse[allExpectedPatternFull]]) → expectedPatternReduced
  117. Take(allSelected, IndexOf[true, allSelected], Length[allSelected] - IndexOf[true, Reverse[allSelected]]) → selectedPatternReduced
  118. Textfield(studentFunc) → inputCoeff
  119. Zip(boxTool[1, 1, A + Vector[Anchor2 - Anchor1] + (1, 1)], A, anchorBlocks1) → fig2Hint
  120. Zip(boxTool[1, 1, A + Vector[Anchor3 - Anchor2] + (1, 1)], A, anchorBlocks2) → fig3Hint
  121. If(stage ≟ 2, -6.5, -1.3) → xMin
  122. If(stage ≟ 2, 33.5, 28) → xMax
  123. If(stage ≟ 2, 12, 10.89) → yMax
  124. Sequence((("SetFilling(A" * B) * ",0.5)"), B, 2, 82) → cmdSetFill
  125. boxTool(1, 1, patternAnchors(E42)) → pulsingBox

AI 绘图提示语参考

绘制一个由方块组成的视觉模式图，用于推导线性方程。图形包含四组按行排列的方块阵列，每组阵列大小递增，形成阶梯状结构。方块分为固定块和可变块，固定块用实心表示，可变块用空心或不同颜色表示。第一组为3×3网格，第二组为5×5网格，第三组为7×7网格，第四组为9×9网格。每组网格中，部分方块被标记为固定，其余为可变，且固定块的位置在每组中保持一致，但整体模式会随机变化。图形下方或旁边可显示对应的数字序列，帮助观察模式与方程的关系。整体布局清晰，适合教学演示。
以上提示语为根据原始绘图命令整理而来，仅供参考。