解方程:使用逆运算

解方程:使用逆运算
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2024-08-01 16:53
本范例演示了如何使用逆运算来解线性方程。学生可以通过调整变量的值来观察方程的变化,并学习如何使用逆运算来求解方程。核心数学概念包括线性方程、逆运算和代数运算。作图要点包括使用 GeoGebra 的 Shuffle、Join、Insert 等命令来构建方程和解方程的过程。适合的学段是初中数学,特别是 5-6 年级学生。

GeoGebra 命令及参数

  1. Shuffle(1…6) → Type1List, {3, 6, 4, 5, 1, 2}
  2. Shuffle(7…12) → Type2List, {10, 9, 8, 11, 7, 12}
  3. Shuffle(19…24) → Type4List, {24, 20, 19, 23, 21, 22}
  4. Join({{3}, Shuffle[{1, 2, 4}]}) → Round1
  5. Insert(Last[Round1], Shuffle[Take[Round1, 1, 3]], RandomElement[2…4]) → Round2
  6. Insert(Last[Round2], Shuffle[Take[Round2, 1, 3]], RandomElement[2…4]) → Round3
  7. Insert(Last[Round3], Shuffle[Take[Round3, 1, 3]], RandomElement[2…4]) → Round4
  8. Insert(Last[Round4], Shuffle[Take[Round4, 1, 3]], RandomElement[2…4]) → Round5
  9. Insert(Last[Round5], Shuffle[Take[Round5, 1, 3]], RandomElement[2…4]) → Round6
  10. Join({{18}, Shuffle[13…17]}) → Type3List
  11. Join({Round1, Round2, Round3, Round4, Round5, Round6}) → TypeList
  12. Sequence(Element[If[TypeList(k) ≟ 1, Type1List, TypeList(k) ≟ 2, Type2List, TypeList(k) ≟ 3, Type3List, Type4List], floor(k / 5) + 1], k, 1, 24) → Reihenfolge
  13. Join({Sequence[3, k, 1, 12], Sequence[4, k, 1, 12]}) → TaskSignList1
  14. SelectedIndex(dropdown1) → indexdd1
  15. Sequence(If[TaskSignList1(k) ≟ 1, 2, TaskSignList1(k) ≟ 2, 1, TaskSignList1(k) ≟ 3, 4, TaskSignList1(k) ≟ 4, 3], k, 1, 24) → UTaskSignList1
  16. Sequence(ParseToNumber[((((Text[Number1List(k)] * "") * Element[SignList, TaskSignList1(k)]) * "") * Text[Number2List(k)])], k, 1, 24) → Number3List
  17. Join({Sequence[1, k, 1, 6], Sequence[2, k, 1, 6], Sequence[1, k, 1, 6], Sequence[2, k, 1, 6]}) → TaskSignList2
  18. SelectedIndex(dropdown3) → indexdd3
  19. Sequence(If[TaskSignList2(k) ≟ 1, 2, TaskSignList2(k) ≟ 2, 1, TaskSignList2(k) ≟ 3, 4, TaskSignList2(k) ≟ 4, 3], k, 1, 24) → UTaskSignList2
  20. Textfield(input4) → InputBox4
  21. Textfield(input3) → InputBox3
  22. Textfield(input2) → InputBox2
  23. Textfield(input1) → InputBox1
  24. Shuffle(1…numberOfQuestions) → randomQuestions, {6, 8, 22, 13, 5, 16, 2, 9, 7, 1, 3, 24, 15, 21, 23, 19, 4, 10, 12, 20, 18, 14, 11, 17}
  25. Textfield(input) → inputBox
  26. Element(randomQuestions, Mod[questionCount - 1, Length[randomQuestions]] + 1) → randomQuestion
  27. Element(SignTextList, TaskSignList1(question)) → txtSign
  28. Midpoint(Corner[txt02, 3], Corner[txt02, 2] + (3.5, 0.05)) → PosSeg2
  29. Segment(PosSeg2, PosSeg2 + (segLength, 0)) → seg2
  30. Sequence(ParseToNumber[((((Text[Number3List(k)] * "") * Element[SignList, TaskSignList2(k)]) * "") * Text[Number4List(k)])], k, 1, 24) → Number5List
  31. Invert(pixMat) → invPixMat
  32. SelectedIndex(dropdown2) → indexdd2
  33. Segment(PosSegSol, PosSegSol + (segLength / 2, 0)) → segSol
  34. Text((((("\textsf{" * SignTextList(UTaskSignList1(question))) * " ") * ReplaceAll[Text[number2], ".", ","]) * "}"), Midpoint[segSol], false, true, 0, 1) → txtSolution3
  35. Segment(PosSeg1, PosSeg1 + (segLength, 0)) → seg1
  36. Text((((("\textsf{" * SignTextList(TaskSignList1(question))) * " ") * ReplaceAll[Text[number2], ".", ","]) * "}"), Midpoint[seg1], false, true, 0, 1) → txt03
  37. Segment(PosSeg21, PosSeg21 + (segLength, 0)) → seg21
  38. Segment(PosSeg11, PosSeg11 + (segLength, 0)) → seg11
  39. Text((((("\textsf{" * SignTextList(TaskSignList2(question))) * " ") * ReplaceAll[Text[number4], ".", ","]) * "}"), Midpoint[seg11], false, true, 0, 1) → txt06
  40. Segment(PosSegSol2, PosSegSol2 + (segLength / 2, 0)) → segSol2
  41. Text((((("\textsf{" * SignTextList(UTaskSignList2(question))) * " ") * ReplaceAll[Text[number4], ".", ","]) * "}"), Midpoint[segSol2], false, true, 0, 1) → txtSolution4
  42. SelectedIndex(dropdown4) → indexdd4
  43. Text(txtSolution6, Midpoint[Corner[txtSolution2, 1], Corner[txtSolution2, 2]] + (0, -1.35), false, true, 0, 0) → txtSolution7

AI 绘图提示语参考

画一个线性方程的解题过程,包含六个步骤。首先,随机生成六个数字,然后根据这些数字生成两个线性方程。接着,使用逆运算逐步解方程,每一步都显示在图上。最后,展示解方程的最终结果。
以上提示语为根据原始绘图命令整理而来,仅供参考。