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二项式乘法教学范例

二项式乘法教学范例
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2024-07-01 15:32
所属专题 Multiplikation von Binomen
①本范例演示二项式乘法的几何解释与计算过程；②涉及核心数学概念包括多项式乘法法则、代数表达式化简、几何图形变换；③构造摘要中用到了Textfield, Shuffle, Text, TextToUnicode, Polygon, Element, Append, Remove, Corner, Point, Circle, Vector, CountIf, Intersection, Defined, Line, Distance, If, CircumcircleArc等GeoGebra命令与对象；④适合初中七、八年级学生，用于理解代数表达式的变形技巧和几何直观。

GeoGebra 命令及参数

  1. Textfield(bInput) → InputBox2
  2. Shuffle({1, 2, 3, 4, 5, 6, 7, 8, 9}) → ListExNumLeicht, {2, 6, 9, 3, 1, 5, 4, 7, 8}
  3. Shuffle({10, 11, 12, 13, 14, 15, 16, 17, 18}) → ListExNumMittel, {10, 14, 17, 13, 18, 11, 15, 16, 12}
  4. Shuffle({19, 20, 21, 22, 23, 24, 25, 26, 27}) → ListExNumSchwer, {25, 20, 24, 23, 19, 27, 22, 26, 21}
  5. Text(I) → IText
  6. TextToUnicode(IText) → ITextUnicode
  7. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  8. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {2, 0, 5, 5, 8, 3, 1, 7, 8, 10, 2, 7, 2, 4, 3, 2, 9, 4, 6, 5, 8, 4, 8, 4, 10, 2, 1, 9, 10, 6, 1, 2, 10, 0, 4, 10, 2, 5, 9, 7, 3, 9, 2, 10, 4, 7, 8, 2, 9, 7, 10, 0, 6, 10, 5, 8, 2, 2, 7, 3, 7, 6, 9, 5, 2, 8, 8, 9, 6, 6, 8, 9, 3, 10, 8, 7, 3, 6, 8, 10, 3, 2, 2, 5, 8, 2, 3, 8, 6, 0, 3, 3, 10, 6, 9, 6, 4, 4, 6, 6}
  9. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  10. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {0, 3, 6, 6, 1, 0, 1, 7, 8, 2, 2, 6, 8, 4, 9, 6, 4, 3, 7, 1, 6, 4, 8, 3, 3, 2, 7, 2, 1, 0, 8, 8, 5, 2, 5, 4, 9, 4, 10, 10, 7, 6, 9, 5, 9, 10, 4, 2, 6, 5, 7, 9, 10, 1, 1, 10, 10, 4, 5, 2, 7, 2, 4, 0, 7, 3, 4, 0, 1, 8, 2, 4, 8, 1, 0, 4, 9, 6, 7, 6, 4, 8, 4, 9, 0, 9, 8, 5, 3, 3, 10, 1, 7, 2, 8, 2, 3, 9, 2, 4}
  11. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  12. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  13. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  14. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  15. Textfield(cInput) → InputBox3
  16. Corner(BildBlue, 1) → controlBlue
  17. Corner(BildGelb, 1) → controlGelb
  18. Corner(BildRosa, 1) → controlRosa
  19. Corner(BildGreen, 1) → controlGreen
  20. Point(line3) → P
  21. Circle(P, Q) → circ
  22. Textfield(inputAdd1) → Eingabefeld1
  23. Textfield(inputAdd2) → Eingabefeld2
  24. Polygon(PtopLeftCornerFeedback_{1} + (0.95, 0), PtopRightCornerFeedback_{1} + (-0.1, 0), PbottomRightCornerFeedback_{1} + (-0.1, 0), PbottomLeftCornerFeedback_{1} + (0.95, 0)) → rectangleCorrect_{1}, strecke4, strecke1, strecke2, strecke3
  25. Polygon(PtopLeftCornerFeedback_{2}, PtopRightCornerFeedback_{2}, PbottomRightCornerFeedback_{2}, PbottomLeftCornerFeedback_{2}) → rectangleCorrect_{2}, ptopleftcornerfeedback_{2}, ptoprightcornerfeedback_{2}, pbottomrightcornerfeedback_{2}, pbottomleftcornerfeedback_{2}
  26. Polygon(PtopLeftCornerFeedback_{3}, PtopRightCornerFeedback_{3}, PbottomRightCornerFeedback_{3}, PbottomLeftCornerFeedback_{3}) → rectangleCorrect_{3}, ptopleftcornerfeedback_{3}, ptoprightcornerfeedback_{3}, pbottomrightcornerfeedback_{3}, pbottomleftcornerfeedback_{3}
  27. Point(circSpecial) → B_2
  28. Point(circ2) → C_2
  29. Point(circ2) → D_2
  30. Point(circ3) → E_2
  31. Point(circ3) → F_2
  32. Point(circ4) → G_2
  33. Point(circ4) → H_2
  34. Point(circ5) → I_2
  35. Point(circ5) → J_2
  36. Point(circ6) → K_2
  37. Point(circ6) → L_2
  38. Point(circ7) → M_2
  39. Point(circ7) → N_2
  40. Point(circ8) → O_2
  41. Point(circ8) → P_2
  42. Point(circ9) → Q_2
  43. Point(circ9) → R_2
  44. Point(circ10) → S_2
  45. Vector(B_2, C_2) → vec7
  46. Vector(D_2, E_2) → vec8
  47. Vector(F_2, G_2) → vec9
  48. Vector(H_2, I_2) → vec1
  49. Vector(J_2, K_2) → vec2
  50. Vector(L_2, M_2) → vec3
  51. Vector(N_2, O_2) → vec4
  52. Vector(P_2, Q_2) → vec5
  53. Vector(R_2, S_2) → vec6
  54. CountIf(a ≟ true, a, bv) → correctProblems
  55. TextToUnicode(Text15) → BuchstabenAlleUnicode
  56. Intersection(BuchstabenAlleUnicode, ITextUnicode) → BuchstabenInputUnicode
  57. TextToUnicode(ListFunktionSol(exNum)) → SolTextUnicode
  58. Intersection(SolTextUnicode, BuchstabenAlleUnicode) → BuchstabenSolUnicode
  59. Defined(I) → fixedhelper
  60. Corner(currentEx, 3) → AnchorBinomMitte
  61. Corner(currentEx, 4) → W_2
  62. Corner(Text3, 3) → Z_2
  63. Line(C_3, xAxis) → f
  64. Textfield(I) → InputBox1
  65. Distance(AnchorBinom2, AnchorBinom3) → a
  66. TextToUnicode(Element[ListeVariablen(1), 1]) → l1
  67. If(blue, controlBlue, gelb, controlGelb, rosa, controlRosa, controlGreen) → controlMaster
  68. Text(Text16, controlMaster + (1.2, -0.1), false, true, -1, 0) → Text17
  69. CircumcircleArc(AnchorBinom1 + derring, AnchorBogerl13, AnchorBinom3) → bogerl1
  70. CircumcircleArc(AnchorBinom1 + derring, AnchorBogerl14, AnchorBinom4) → bogerl2
  71. CircumcircleArc(Mirror[AnchorBinom2 + derring, f], Mirror[AnchorBogerl24, f], Mirror[AnchorBinom4, f]) → bogerl4
  72. CircumcircleArc(Mirror[AnchorBinom2 + derring, f], Mirror[AnchorBogerl23, f], Mirror[AnchorBinom3, f]) → bogerl3
  73. If(questionCount ≟ 1, circSpecial, questionCount ≟ 6, circ6, questionCount ≟ 7, circ7, questionCount ≟ 8, circ8, questionCount ≟ 9, circ9, questionCount ≟ 10, circ10, questionCount ≟ 2, circ2, questionCount ≟ 3, circ3, questionCount ≟ 4, circ4, questionCount ≟ 5, circ5) → Golasso