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世界之旅：整数的加减法与几何作图

世界之旅：整数的加减法与几何作图
几何画板及绘图内容加载中，请稍等……
2026-02-18 20:36
所属专题 Addieren und Subtrahieren von ganzen und rationalen Zahlen
这个范例演示了如何通过几何作图来理解整数的加减法。核心数学概念包括加法、减法以及几何构造。作图要点涉及使用GeoGebra命令如Corner、Point、Vector等来创建图形对象。适合初中生或数学爱好者学习几何与算术的结合。

GeoGebra 命令及参数

  1. Corner(FahneBlue, 1) → controlBlue
  2. Corner(FahneGelb, 1) → controlGelb
  3. Corner(FahneRosa, 1) → controlRosa
  4. Corner(FahneGreen, 1) → controlGreen
  5. Point(Kreis1) → Pfeil1A
  6. Point(Kreis2) → Pfeil1E
  7. Point(Kreis2) → Pfeil2A
  8. Point(Kreis3) → Pfeil2E
  9. Point(Kreis3) → Pfeil3A
  10. Point(Kreis4) → Pfeil3E
  11. Point(Kreis4) → Pfeil4A
  12. Point(Kreis5) → Pfeil4E
  13. Point(Kreis5) → Pfeil5A
  14. Point(Kreis6) → Pfeil5E
  15. Point(Kreis6) → Pfeil6A
  16. Point(Kreis7) → Pfeil6E
  17. Point(Kreis7) → Pfeil7A
  18. Point(Kreis8) → Pfeil7E
  19. Point(Kreis8) → Pfeil8A
  20. Point(Kreis9) → Pfeil8E
  21. Point(Kreis9) → Pfeil9A
  22. Point(Kreis10) → Pfeil9E
  23. Vector(Pfeil1A, Pfeil1E) → Pfeil1
  24. Vector(Pfeil2A, Pfeil2E) → Pfeil2
  25. Vector(Pfeil3A, Pfeil3E) → Pfeil3
  26. Vector(Pfeil4A, Pfeil4E) → Pfeil4
  27. Vector(Pfeil5A, Pfeil5E) → Pfeil5
  28. Vector(Pfeil6A, Pfeil6E) → Pfeil6
  29. Vector(Pfeil7A, Pfeil7E) → Pfeil7
  30. Vector(Pfeil8A, Pfeil8E) → Pfeil8
  31. Vector(Pfeil9A, Pfeil9E) → Pfeil9
  32. CountIf(a ≟ true, a, allCorrects) → correctCount
  33. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  34. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  35. Textfield(input) → inputBox
  36. Join(Sequence[Shuffle[1…4], k, 1, 60]) → listVZ
  37. Split(Text[inputBox], {""}) → l1
  38. CountIf(x ≟ "/", l1) → nBruch
  39. Join(Sequence[Shuffle[10…20], k, 1, 60]) → listZahlen2
  40. Join(Sequence[Shuffle[1…10], k, 1, 60]) → listZahlen1
  41. If(questionCount ∈ {1, 2, 4, 5, 8, 9}, listZahlen1, listZahlen2) → listZahlen
  42. If(questionCount < 4, 0, actualNumbers(3)) → num3
  43. If(questionCount < 8, 0, actualNumbers(4)) → num4
  44. If(questionCount ≤ 3, listVZ(actualQuestion), listVZ((3 * actualQuestion))) → VZ2
  45. If(questionCount ≤ 3, listVZ(actualQuestion + 1), listVZ((3 * actualQuestion) + 1)) → VZ3
  46. If(questionCount ≤ 3, listVZ(actualQuestion + 2), listVZ((3 * actualQuestion) + 2)) → VZ4
  47. If(VZ1 ∈ {1, 2}, num1, (-num1)) → solution1
  48. If(VZ1 ∈ {1, 2}, num1, (-num1)) → actualNum1
  49. If(VZ2 ∈ {1, 4}, num2, (-num2)) → actualNum2
  50. If(VZ3 ∈ {1, 4}, num3, (-num3)) → actualNum3
  51. If(VZ4 ∈ {1, 4}, num4, (-num4)) → actualNum4
  52. If(Defined[input3], If[SelectedIndex[drop2] ≟ 2, input3, (-input3)], 0) → inputSet2
  53. If(Defined[input4], If[SelectedIndex[drop3] ≟ 2, input4, (-input4)], 0) → inputSet3
  54. If(Defined[input2], If[SelectedIndex[drop1] ≟ 2, input2, (-input2)], 0) → inputSet1
  55. CountIf(x ≟ "-", Split[Text[inputBox], {""}]) → nMinus
  56. Textfield(input1) → inputBox1
  57. Textfield(input4) → inputBox4
  58. Textfield(input3) → inputBox3
  59. Textfield(input2) → inputBox2
  60. If(pickedBlue, controlBlue, pickedGelb, controlGelb, pickedRosa, controlRosa, controlGreen) → controlMaster
  61. Element({Kreis1, Kreis2, Kreis3, Kreis4, Kreis5, Kreis6, Kreis7, Kreis8, Kreis9, Kreis10}, questionCount) → NextPosition
  62. Text(inputBox) → txtInputBox
  63. ParseToNumber(ReplaceAll[txtInputBox, ",", "."]) → a
  64. If(questionCount ≤ 3, 2, questionCount ≤ 7, 3, 4) → nNumbers