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Journey Around the World: Adding and Subtracting Whole Numbers

Journey Around the World: Adding and Subtracting Whole Numbers
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2026-02-18 20:36
In collections Addieren und Subtrahieren von ganzen und rationalen Zahlen
This example demonstrates how to understand addition and subtraction of whole numbers through geometric construction. Key mathematical concepts include addition, subtraction, and geometric construction. Construction involves using GeoGebra commands such as Corner, Point, Vector, etc. Suitable for middle school students or math enthusiasts learning the combination of geometry and arithmetic.

GeoGebra Commands & Parameters

  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