积极 AI Logo 积极 AI

数轴上的变化图形

数轴上的变化图形
几何画板及绘图内容加载中，请稍等……
2026-01-05 23:43
所属专题 Addieren und Subtrahieren von ganzen und rationalen Zahlen
本范例演示了如何在数轴上绘制变化图形，展示数轴上的变化。核心数学概念包括整数的加减运算、数轴上的点的移动。作图要点包括使用 GeoGebra 的 Sequence、Element、Textfield 等命令和对象。适合的学段或用途包括初中数学教育，特别是数轴和整数运算的教学。

GeoGebra 命令及参数

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {5, 8, 10, 3, 10, 9, 1, 6, 1, 3}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. 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
  5. 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
  6. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte
  7. Ellipse(Midpoint[PointsAZK(1), PointsAZK(2)] + (sqrt(Distance[PointsAZK(2), Midpoint[PointsAZK(1), PointsAZK(2)]]^(2) - Distance[PointsBZK(2), Midpoint[PointsAZK(1), PointsAZK(2)]]^(2)), 0), Midpoint[PointsAZK(1), PointsAZK(2)] + ((-sqrt(Distance[PointsAZK(2), Midpoint[PointsAZK(1), PointsAZK(2)]]^(2) - Distance[PointsBZK(2), Midpoint[PointsAZK(1), PointsAZK(2)]]^(2))), 0), Distance[PointsAZK(1), PointsAZK(2)] / 2) → ellZK
  8. If(step < 5, -7, 3) → numberStone1
  9. If(step < 5, 10, -8) → numberStone2
  10. If(step < 5, -5, 2) → numberStone3
  11. If(step < 5, -8, -6) → numberStone4
  12. If(step < 5, 3, 7) → numberStone5
  13. If(step < 5, 5, -2) → numberStone6
  14. Sequence(IsInRegion[AllPStones(k), RegionZK(1)], k, 1, Length[AllPStones]) → StoneInRegion
  15. Sum(Sequence[If[StoneInRegion(k), AllNumbersStones(k), 0], k, 1, Length[AllNumbersStones]]) → actualTemperature
  16. Sequence(PointsThermoEnd(1) + (k * (0, Distance[PointsThermoEnd(1), PointsThermoEnd(2)] / (thermoEnd - thermoStart))), k, 0, thermoEnd - thermoStart, 1) → PointsThermo
  17. RemoveUndefined(Sequence[If[Mod[TemperatureList(k), thermoStepMark] ≟ 0, Segment[PointsThermo(k) + (((-segLengthThermo)) / 2, 0), PointsThermo(k) + (segLengthThermo / 2, 0)]], k, 1, Length[PointsThermo]]) → segMarkThermo
  18. RemoveUndefined(Sequence[If[Mod[TemperatureList(k), thermoStepCap] ≟ 0, Text[((("\textsf{\(" * If[TemperatureList(k) > 0, "+", ""]) * TemperatureList(k)) * "\)}"), PointsThermo(k) + ((6 / 5 * segLengthThermo), 0.05), false, true, 0, 0]], k, 1, Length[PointsThermo]]) → CapThermo
  19. Text(((("\textsf{\bold{\(" * If[actualTemperature > 0, "+", ""]) * actualTemperature) * "\)}}"), PointsThermo(IndexOf[actualTemperature, TemperatureList]) + ((-6 / 5 * segLengthThermo), 0.05), false, true, 0, 0) → CapActualTemperature
  20. Sequence(((dimStoneA * cos(k°)), (dimStoneB * sin(k°))), k, 0, 360, 5) → PointStone
  21. Text((("\textsf{\bold{\textcolor{white}{" * If[showMinusStone, (If[numberStone1 > 0, "+", numberStone1 ≟ 0, "\phantom{+}", "\(-\)"] * abs(numberStone1)), (abs(numberStone1) * "")]) * "}}}"), PStone1 + (0, 0.05), false, true, 0, 0) → txtStone1
  22. Text((("\textsf{\bold{\textcolor{white}{" * If[showMinusStone, (If[numberStone2 > 0, "+", numberStone2 ≟ 0, "\phantom{+}", "\(-\)"] * abs(numberStone2)), (abs(numberStone2) * "")]) * "}}}"), PStone2 + (0, 0.05), false, true, 0, 0) → txtStone2
  23. Text((("\textsf{\bold{\textcolor{white}{" * If[showMinusStone, (If[numberStone3 > 0, "+", numberStone3 ≟ 0, "\phantom{+}", "\(-\)"] * abs(numberStone3)), (abs(numberStone3) * "")]) * "}}}"), PStone3 + (0, 0.05), false, true, 0, 0) → txtStone3
  24. Text((("\textsf{\bold{\textcolor{white}{" * If[showMinusStone, (If[numberStone4 > 0, "+", numberStone4 ≟ 0, "\phantom{+}", "\(-\)"] * abs(numberStone4)), (abs(numberStone4) * "")]) * "}}}"), PStone4 + (0, 0.05), false, true, 0, 0) → txtStone4
  25. Text((("\textsf{\bold{\textcolor{white}{" * If[showMinusStone, (If[numberStone5 > 0, "+", numberStone5 ≟ 0, "\phantom{+}", "\(-\)"] * abs(numberStone5)), (abs(numberStone5) * "")]) * "}}}"), PStone5 + (0, 0.05), false, true, 0, 0) → txtStone5
  26. Text((("\textsf{\bold{\textcolor{white}{" * If[showMinusStone, (If[numberStone6 > 0, "+", numberStone6 ≟ 0, "\phantom{+}", "\(-\)"] * abs(numberStone6)), (abs(numberStone6) * "")]) * "}}}"), PStone6 + (0, 0.05), false, true, 0, 0) → txtStone6
  27. Text((("\textsf{\bold{\textcolor{white}{" * If[showMinusStone, (If[numberStone7 > 0, "+", numberStone7 ≟ 0, "\phantom{+}", "\(-\)"] * abs(numberStone7)), (abs(numberStone7) * "")]) * "}}}"), PStone7 + (0, 0.05), false, true, 0, 0) → txtStone7
  28. Textfield(input021) → InputBox021
  29. Textfield(input031) → InputBox031
  30. Textfield(input041) → InputBox041
  31. Textfield(input051) → InputBox051
  32. Textfield(input061) → InputBox061
  33. Textfield(input071) → InputBox071
  34. SelectedIndex(dropdown031) → index031
  35. If(actualTemperature > -2, index031 ≟ 2, index031 ≟ 3) → correctdd031
  36. SelectedIndex(dropdown061) → index061
  37. If(actualTemperature > -4, index061 ≟ 2, index061 ≟ 3) → correctdd061
  38. SelectedIndex(dropdown081) → index081
  39. SelectedIndex(dropdown082) → index082
  40. Segment(ZGStart + ((-ZGEdge), 0), ZGStart + (ZGLength + ZGEdge, 0)) → ZGSeg
  41. Sequence(ZGStart + (k / (ZGMax - ZGMin) * (ZGLength, 0)), k, 0, ZGMax - ZGMin) → ZGPoints
  42. Sequence(Segment[ZGPoints(k) + (0, If[Mod[k, ZGCap] ≟ 1, ZGDis02, ZGDis01]), ZGPoints(k) - (0, If[Mod[k, ZGCap] ≟ 1, ZGDis02, ZGDis01])], k, 1, ZGMax - ZGMin + 1) → ZGSegList
  43. Sequence(Text[(("\textsf{\small{\bold{\(" * (ZGMin + k - 1)) * "\)}}}"), ZGPoints(k) + (If[ZGMin + k - 1 < 0, -0.15, 0], (-ZGDis02)), false, true, 0, -1], k, 1, ZGMax - ZGMin + 1, ZGCap) → ZGCapList
  44. Text("\textsf{\textcolor{db6114}{\small{\bold{\(-2\)}}}}", ZGPoints(ZGMin - 2 - 1) + (If[ZGMin - 2 - 1 < 0, -0.15, 0], (-ZGDis02)), false, true, 0, -1) → CapZG02
  45. Text((("\textsf{\bold{\textcolor{white}{" * If[showMinusStone, (If[number031 > 0, "+", number031 ≟ 0, "\phantom{+}", "\(-\)"] * abs(number031)), (abs(number031) * "")]) * "}}}"), Pos031 + (0, 0.05), false, true, 0, 0) → txtStone031
  46. Segment(PosZG02 + (0, ZGDis02 + 0.25), PosZG04 + (0, ZGDis02 + 0.25)) → seg03
  47. Text((((("\textsf{\textcolor{db6114}{\small{\bold{\(" * If[actualTemperature < -2, "-", "+"]) * "\) ") * abs(number031)) * "}}}}"), Midpoint[seg03], false, true, 0, 1) → CapZG03
  48. Text((("\textsf{\textcolor{db6114}{\small{\bold{\(" * actualTemperature) * "\)}}}}"), ZGPoints(ZGMin + actualTemperature - 1) + (If[actualTemperature < 0, -0.15, 0], (-ZGDis02)), false, true, 0, -1) → CapZG04
  49. Segment(ZGStart081 + ((-ZGEdge), 0), ZGStart081 + (ZGLength08 + ZGEdge, 0)) → ZGSeg081
  50. Segment(ZGStart082 + ((-ZGEdge), 0), ZGStart082 + (ZGLength08 + ZGEdge, 0)) → ZGSeg082
  51. Sequence(ZGStart081 + (k / (ZGMax - ZGMin) * (ZGLength08, 0)), k, 0, ZGMax - ZGMin) → ZGPoints081
  52. Sequence(ZGStart082 + (k / (ZGMax - ZGMin) * (ZGLength08, 0)), k, 0, ZGMax - ZGMin) → ZGPoints082
  53. Sequence(Segment[ZGPoints081(k) + (0, If[Mod[k, ZGCap] ≟ 1, ZGDis02, ZGDis01]), ZGPoints081(k) - (0, If[Mod[k, ZGCap] ≟ 1, ZGDis02, ZGDis01])], k, 1, ZGMax - ZGMin + 1) → ZGSegList081
  54. Sequence(Segment[ZGPoints082(k) + (0, If[Mod[k, ZGCap] ≟ 1, ZGDis02, ZGDis01]), ZGPoints082(k) - (0, If[Mod[k, ZGCap] ≟ 1, ZGDis02, ZGDis01])], k, 1, ZGMax - ZGMin + 1) → ZGSegList082
  55. Sequence(Text[(("\textsf{\small{\bold{\(" * (ZGMin + k - 1)) * "\)}}}"), ZGPoints081(k) + (If[ZGMin + k - 1 < 0, -0.15, 0], (-ZGDis02)), false, true, 0, -1], k, 1, ZGMax - ZGMin + 1, ZGCap) → ZGCapList081
  56. Sequence(Text[(("\textsf{\small{\bold{\(" * (ZGMin + k - 1)) * "\)}}}"), ZGPoints082(k) + (If[ZGMin + k - 1 < 0, -0.15, 0], (-ZGDis02)), false, true, 0, -1], k, 1, ZGMax - ZGMin + 1, ZGCap) → ZGCapList082
  57. If(step ≟ 2, correct021, step ≟ 7, correct071, true, step ≟ 3, correct031 ∧ correctdd031, step ≟ 4, correct041, step ≟ 5, correct051, step ≟ 6, correct061 ∧ correctdd061) → clickableBtnNext
  58. Text((("\textsf{\bold{\textcolor{white}{" * If[showMinusStone, (If[number061 > 0, "+", number061 ≟ 0, "\phantom{+}", "\(-\)"] * abs(number061)), (abs(number061) * "")]) * "}}}"), Pos061 + (0, 0.05), false, true, 0, 0) → txtStone061
  59. Segment(PosZG05 + (0, ZGDis02 + 0.25), PosZG07 + (0, ZGDis02 + 0.25)) → seg06
  60. Text((((("\textsf{\textcolor{db6114}{\small{\bold{\(" * If[actualTemperature < -4, "-", "+"]) * "\) ") * abs(number061)) * "}}}}"), Midpoint[seg06], false, true, 0, 1) → CapZG06
  61. Text((("\textsf{\textcolor{db6114}{\small{\bold{\(" * actualTemperature) * "\)}}}}"), ZGPoints(ZGMin + actualTemperature - 1) + (If[actualTemperature < 0, -0.15, 0], (-ZGDis02)), false, true, 0, -1) → CapZG07
  62. Segment(PosZG081(1) + (0, ZGDis02 + 0.25), PosZG081(2) + (0, ZGDis02 + 0.25)) → seg081
  63. Segment(PosZG082(1) + (0, ZGDis02 + 0.25), PosZG082(2) + (0, ZGDis02 + 0.25)) → seg082
  64. Text("\textsf{\textcolor{db6114}{\small{\bold{\(-3\)}}}}", ZGPoints(ZGMin - 3 - 1) + (If[-4 < 0, -0.15, 0], (-ZGDis02)), false, true, 0, -1) → CapZG05
  65. If(step ≟ 2 ∨ step ≟ 5, (4.75, 8.25), step ≟ 3 ∨ step ≟ 6, (2, 6.25), step ≟ 4 ∨ step ≟ 7, (2, 4), (1, 1)) → PosBtnShowSolution