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用逆运算解线性方程：箭头表示与纠错

用逆运算解线性方程：箭头表示与纠错
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2024-07-30 21:07
函数变换不等式几何作图
所属专题 Gleichungen lösen mit Umkehroperationen
这个范例演示如何通过“逆运算”把线性方程逐步化简到解，并用箭头表示正向变换与反向还原的过程。核心数学概念包括：线性方程的求解、等式性质、加法/减法与乘法/除法的逆运算，以及用错误情境（两位学生的错误）训练对等式变形的审查能力。作图与交互要点：从构造摘要可见它使用 Sequence、Element 组织题目步骤/选项，Textfield 与 InputBox 采集用户输入；通过 SelectedIndex 控制多选题的选择；用 Segment、PolyLine 以及箭头/路径类图形呈现步骤流向；借助 Invert 对箭头或变换顺序进行反转；并使用 If 来根据答题正确性切换反馈文本（如 txtFeedback、txtSolution、correct）、以及用 validate 进行提交验证，同时设置 attemptCount 与 questionCount 统计作答进度。适合小学五六年级到初中入门阶段的数学课（方程与逆运算教学、课堂练习或互动测验）。

GeoGebra 命令及参数

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {10, 9, 8, 5, 4, 9, 9, 4, 1, 1}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. Textfield(input031) → InputBox031
  5. Textfield(input032) → InputBox032
  6. Textfield(input033) → InputBox033
  7. Textfield(input041) → InputBox041
  8. Textfield(input042) → InputBox042
  9. Textfield(input043) → InputBox043
  10. Textfield(input044) → InputBox044
  11. Textfield(input091) → InputBox091
  12. Textfield(input092) → InputBox092
  13. Textfield(input093) → InputBox093
  14. Textfield(input101) → InputBox101
  15. Textfield(input102) → InputBox102
  16. Textfield(input103) → InputBox103
  17. Textfield(input104) → InputBox104
  18. Textfield(input131) → InputBox131
  19. Textfield(input132) → InputBox132
  20. Textfield(input133) → InputBox133
  21. Textfield(input141) → InputBox141
  22. Textfield(input142) → InputBox142
  23. Textfield(input143) → InputBox143
  24. Textfield(input144) → InputBox144
  25. Textfield(input171) → InputBox171
  26. Textfield(input172) → InputBox172
  27. Textfield(input173) → InputBox173
  28. Textfield(input181) → InputBox181
  29. Textfield(input182) → InputBox182
  30. Textfield(input183) → InputBox183
  31. Textfield(input184) → InputBox184
  32. SelectedIndex(dropdown031) → index031
  33. SelectedIndex(dropdown032) → index032
  34. SelectedIndex(dropdown041) → index041
  35. SelectedIndex(dropdown042) → index042
  36. SelectedIndex(dropdown091) → index091
  37. SelectedIndex(dropdown092) → index092
  38. SelectedIndex(dropdown101) → index101
  39. SelectedIndex(dropdown102) → index102
  40. SelectedIndex(dropdown131) → index131
  41. SelectedIndex(dropdown132) → index132
  42. SelectedIndex(dropdown141) → index141
  43. SelectedIndex(dropdown142) → index142
  44. SelectedIndex(dropdown171) → index171
  45. SelectedIndex(dropdown172) → index172
  46. SelectedIndex(dropdown181) → index181
  47. SelectedIndex(dropdown182) → index182
  48. Segment(PosSeg1, PosSeg1 + (segLength, 0)) → seg1
  49. Segment(PosSeg2, PosSeg2 + (segLength, 0)) → seg2
  50. Invert(pixMat) → invPixMat
  51. Segment(PosSeg3, PosSeg3 + (segLength, 0)) → seg3
  52. Segment(PosSeg4, PosSeg4 + (segLength, 0)) → seg4
  53. Text((("\textsf{" * number3List(Task)) * "}"), Point[seg3, 1] + (0.1, 0.05), false, true, 1, 0) → txtRes1
  54. Segment(PosSegCalc1, PosSegCalc1 + (segLengthCalc, 0)) → segCalc1
  55. Segment(PosSegCalc2, PosSegCalc2 + (segLengthCalc, 0)) → segCalc2
  56. Text((("\textsf{" * number3List(Task)) * "}"), Point[segCalc2, 1] + (0.1, 0.05), false, true, 1, 0) → txtCalc3
  57. Segment(PosSegCalc2 + (0, (-dis2)), PosSegCalc2 + (segLengthCalc, (-dis2))) → segCalc3
  58. Segment(PosSegCalc1 + (0, (-dis2)), PosSegCalc1 + (segLengthCalc, (-dis2))) → segCalc4
  59. Text((("\textsf{" * number3List(Task)) * "}"), Point[segCalc3, 1] + (0.1, 0.05), false, true, 1, 0) → txtCalc5
  60. Text((("\textsf{" * number4List(Task)) * "}"), Midpoint[Point[segCalc4, 1] + (0, 0.1), Point[segCalc3, 0]], false, true, 0, 0) → txtCalc6
  61. PolyLine(PosSB, Corner[txt021, 1] + (-0.1 + 1.75, 0.05), Corner[txt021, 1] + (-0.1, 0.05), Corner[txt021, 4] + (-0.1, 0.05), Corner[txt021, 3] + (0, 0.05), Corner[txt021, 2] + (0, 0), Corner[txt021, 1] + (-0.1 + 2.5, 0.05), PosSB) → sb02
  62. PolyLine(PosSB, Corner[txt061, 1] + (-0.1 + 1.75, 0.05), Corner[txt061, 1] + (-0.1, 0.05), Corner[txt061, 4] + (-0.1, 0.05), Corner[txt061, 3] + (0, 0.05), Corner[txt061, 2] + (0, 0), Corner[txt061, 1] + (-0.1 + 2.5, 0.05), PosSB) → sb06
  63. PolyLine(PosSB, Corner[txt081, 1] + (-0.1 + 1.75, 0.05), Corner[txt081, 1] + (-0.1, 0.05), Corner[txt081, 4] + (-0.1, 0.05), Corner[txt081, 3] + (0, 0.05), Corner[txt081, 2] + (0, 0), Corner[txt081, 1] + (-0.1 + 2.5, 0.05), PosSB) → sb08
  64. PolyLine(PosSB, Corner[txt131, 1] + (-0.1 + 1.75, 0.05), Corner[txt131, 1] + (-0.1, 0.05), Corner[txt131, 4] + (-0.1, 0.05), Corner[txt131, 3] + (0, 0.05), Corner[txt131, 2] + (0, 0), Corner[txt131, 1] + (-0.1 + 2.5, 0.05), PosSB) → sb13
  65. PolyLine(PosSB, Corner[txt171, 1] + (-0.1 + 1.75, 0.05), Corner[txt171, 1] + (-0.1, 0.05), Corner[txt171, 4] + (-0.1, 0.05), Corner[txt171, 3] + (0, 0.05), Corner[txt171, 2] + (0, 0), Corner[txt171, 1] + (-0.1 + 2.5, 0.05), PosSB) → sb17
  66. If(step ≟ 3, correct031 ∧ correctdd032 ∧ correct033, step ≟ 14, correct141 ∧ correctdd141 ∧ correct142 ∧ correct143 ∧ correctdd142 ∧ correct144, step ≟ 17, correctdd171 ∧ correct171 ∧ correctdd172 ∧ correct172 ∧ correct173, step ≟ 18, correct181 ∧ correctdd181 ∧ correct182 ∧ correct183 ∧ correctdd182 ∧ correct184, true, step ≟ 4, correct041 ∧ correctdd041 ∧ correct042 ∧ correct043 ∧ correctdd042 ∧ correct044, step ≟ 9, correctdd091 ∧ correct091 ∧ correctdd092 ∧ correct092 ∧ correct093, step ≟ 10, correct101 ∧ correctdd101 ∧ correct102 ∧ correct103 ∧ correctdd102 ∧ correct104, step ≟ 13, correctdd131 ∧ correct131 ∧ correctdd132 ∧ correct132 ∧ correct133) → clickableBtnNext
  67. PolyLine(PosSB, Corner[txt55, 1] + (-0.1 + 1.75, 0.05), Corner[txt55, 1] + (-0.1, 0.05), Corner[txt55, 4] + (-0.1, 0.05), Corner[txt55, 3] + (0, 0.05), Corner[txt55, 2] + (0, 0), Corner[txt55, 1] + (-0.1 + 2.5, 0.05), PosSB) → sb55
  68. PolyLine(PosSB, Corner[txt071, 1] + (-0.1 + 1.75, 0.05), Corner[txt071, 1] + (-0.1, 0.05), Corner[txt071, 4] + (-0.1, 0.05), Corner[txt071, 3] + (0, 0.05), Corner[txt071, 2] + (0, 0), Corner[txt071, 1] + (-0.1 + 2.5, 0.05), PosSB) → sb07
  69. PolyLine(PosSB, Corner[txt201, 1] + (0.5, -0.1), Corner[txt201, 2] + (0.1, -0.1), Corner[txt201, 3] + (0.1, 0.1), Corner[txt201, 4] + (-0.1, 0.1), Corner[txt201, 1] + (-0.1, -0.1), PosSB) → sb20
  70. Segment(Midpoint[Corner[txt203, 3], Corner[txt203, 2]] + (0.25, 0.04), Midpoint[Corner[txt203, 3], Corner[txt203, 2]] + (0.25, 0.04) + (segLength, 0)) → seg201
  71. Segment(Point[seg201, 0] + (segLength + 0.25, -0.4) + (1.05 + 0.25, 0.4), Point[seg201, 0] + (segLength + 0.25, -0.4) + (1.05 + 0.25, 0.4) + (segLength, 0)) → seg202
  72. Segment(Midpoint[Corner[txt204, 3], Corner[txt204, 2]] + (0.25, 0.04), Midpoint[Corner[txt204, 3], Corner[txt204, 2]] + (0.25, 0.04) + (segLength, 0)) → seg204
  73. Segment(Point[seg204, 0] + (segLength + 0.25, -0.4) + (1.05 + 0.25, 0.4), Point[seg204, 0] + (segLength + 0.25, -0.4) + (1.05 + 0.25, 0.4) + (segLength, 0)) → seg203

AI 绘图提示语参考

画一个线性方程求解的演示图，包含随机生成的数字序列，用箭头表示每一步的逆操作，展示如何通过逆向操作逐步解决方程。使用文本框收集用户输入，下拉菜单选择操作，用线段绘制箭头指示步骤方向，根据用户答案显示正确或错误的反馈信息，整体呈现方程求解的过程和常见错误检查。
以上提示语为根据原始绘图命令整理而来，仅供参考。