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整数集合

整数集合
几何画板及绘图内容加载中，请稍等……
2024-05-23 18:24
函数数列解析几何几何作图滑块动画
所属专题 Ganze Zahlen & Arbeiten mit der Zahlengerade
这个范例演示了如何使用 GeoGebra 探索整数集合的概念。涉及的核心数学概念包括整数的定义、在数轴上的表示以及整数的比较和排序。作图要点——从下方『构造摘要』提炼用到了哪些 GeoGebra 命令/对象：Sequence, Element, Textfield, SpeechBubbleLeft, If, Segment, RemoveUndefined, SelectedIndex, CircleArc, Text, PolyLine；对象：txt011, btnBack, attemptCount, questionCount, correct, randomNumbers, rectangleFeedback, txtSolution, txtHint, randomNumber, btnNew, btnNext, txtFeedback, validate, imgInfoA, imgInfoB, txtInfo, step, imgInfo, input, showsolution, btnShowSolution, inputBox, ca800x600, PosMonster1, imgMonster, PosMonster2, sbwidth01, sbwidth02, sbwidth03, sbwidth04, sbwidth05, sbwidth06, sbwidth07, sbwidth08, sbwidth09, sbwidth10, sbheight01, sbheight02, sbheight03。适合的学段或用途：小学5-6年级，用于教授学生如何使用数轴比较和排序整数，以及如何在数学情境之外解释整数。

GeoGebra 命令及参数

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {5, 5, 1, 4, 8, 3, 5, 3, 7, 10}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. SpeechBubbleLeft(PosSB, sbwidth, sbheight) → SB
  5. If(step ≟ 5, (8, 6), (8, 3.5)) → Origin1
  6. If(step ≟ 2.5 ∨ step ≟ 3 ∨ step ≟ 11, Origin1 + (0, 2.75), step ≟ 6 ∨ step ≟ 7 ∨ step ≟ 8 ∨ step ≟ 9 ∨ step ≟ 10, Origin1 + (0, 0.25), Origin1 + (0, (-disY) - 0.5 + If[step ≟ 3, -1, 0])) → Origin2
  7. Sequence(Origin1 + ((k * disX), 0), k, 0, 10) → PointListAxis1
  8. Sequence(Origin2 + ((k * disX), 0), k, -10, 10) → PointListAxis2
  9. Sequence(Origin3 + ((k * disX), 0), k, 0, 10) → PointListAxis3
  10. Sequence(Text[(("$\textsf{" * k) * "}$"), PointListAxis1(k + 1) + (0, (-segLength)), false, true, 0, -1], k, 0, Length[PointListAxis1]) → CapAxis1
  11. Sequence(Text[(("$\textsf{" * k) * "}$"), PointListAxis3(k + 1) + (0, (-segLength)), false, true, 0, -1], k, 0, Length[PointListAxis3]) → CapAxis3
  12. Sequence(Text[(("$\textsf{" * k) * "}$"), PointListAxis2(k + 11) + (0, (-segLength)), false, true, 0, -1], k, 0, Length[PointListAxis1]) → CapAxis2P
  13. Sequence(Text[(("$\textsf{\(-" * k) * "\)}$"), PointListAxis2(11 - k) + (-0.155, (-segLength)), false, true, 0, -1], k, 1, Length[PointListAxis1]) → CapAxis2N
  14. Segment(Origin2, Origin2 + ((-10 * disX) - 0.5, 0)) → SegNAxis2
  15. Segment(Origin2, Origin2 + ((10 * disX) + 0.5, 0)) → SegPAxis2
  16. Segment(Origin3, Origin3 + ((10 * disX) + 0.5, 0)) → SegPAxis3
  17. Segment(Origin1, Origin1 + ((10 * disX) + 0.5, 0)) → SegPAxis1
  18. RemoveUndefined(Unique[{input021, input022, input023}]) → Task2List
  19. Textfield(input021) → InputBox021
  20. Textfield(input022) → InputBox022
  21. Textfield(input023) → InputBox023
  22. RemoveUndefined(Unique[{input031, input032, input033}]) → Task3List
  23. Textfield(input031) → InputBox031
  24. Textfield(input032) → InputBox032
  25. Textfield(input033) → InputBox033
  26. SelectedIndex(dropdown051) → index051
  27. SelectedIndex(dropdown052) → index052
  28. Textfield(input061) → InputBox061
  29. CircleArc(Midpoint[PointListAxis2(18), PointListAxis2(19)] + (0, 0.5), PointListAxis2(19) + (0, 0.5), PointListAxis2(18) + (0, 0.5)) → arc067
  30. Segment(PointListAxis2(19) + (0, 0.5), PointListAxis2(19) + (0, 0.4)) → arrow067
  31. Textfield(input071) → InputBox071
  32. CircleArc(Midpoint[PointListAxis2(7), PointListAxis2(8)] + (0, 0.5), PointListAxis2(8) + (0, 0.5), PointListAxis2(7) + (0, 0.5)) → arc074
  33. Segment(PointListAxis2(8) + (0, 0.5), PointListAxis2(8) + (0, 0.4)) → arrow074
  34. SelectedIndex(dropdown072) → index072
  35. Textfield(input081) → InputBox081
  36. Textfield(input091) → InputBox091
  37. Textfield(input101) → InputBox101
  38. Textfield(input102) → InputBox102
  39. Textfield(input103) → InputBox103
  40. Textfield(input104) → InputBox104
  41. CircleArc(Midpoint[PointListAxis2(2), PointListAxis2(1)] + (0, 0.5), PointListAxis2(2) + (0, 0.5), PointListAxis2(1) + (0, 0.5)) → arc091
  42. Segment(PointListAxis2(1) + (0, 0.5), PointListAxis2(1) + (0, 0.4)) → arrow0910
  43. SelectedIndex(dropdown092) → index092
  44. RemoveUndefined(Unique[{input101, input102, input103, input104}]) → Task10List
  45. If(step ≟ 2, correct021 ∧ correct022 ∧ correct023, step ≟ 7, correct071 ∧ correctdd072, step ≟ 8, correct081, step ≟ 9, correct091 ∧ correctdd092, step ≟ 10, correct101 ∧ correct102 ∧ correct103 ∧ correct104, true, step ≟ 2.5, anim3 ≟ 3, step ≟ 3, correct031 ∧ correct032 ∧ correct033, step ≟ 5, correctdd05 ∧ bewegung ≟ 1, step ≟ 6, correct061) → clickableBtnNext
  46. If(step ≟ 2, PosSol2, step ≟ 9, PosSol8, PosSol10, step ≟ 3, PosSol3, step ≟ 6, PosSol6, step ≟ 7, PosSol7, step ≟ 8, PosSol8) → PosSol
  47. Sequence(Segment[PointListAxis1(k) + (0, (-If[k ≟ 1, segLength0, segLength])), PointListAxis1(k) + (0, If[k ≟ 1, segLength0, segLength])], k, 1, Length[PointListAxis1]) → segList1
  48. Sequence(Segment[PointListAxis2(k) + (0, (-If[k ≟ 11, segLength0, segLength])), PointListAxis2(k) + (0, If[k ≟ 11, segLength0, segLength])], k, 1, Length[PointListAxis2]) → segList2
  49. Sequence(Segment[PointListAxis3(k) + (0, (-If[k ≟ 1, segLength0, segLength])), PointListAxis3(k) + (0, If[k ≟ 1, segLength0, segLength])], k, 1, Length[PointListAxis3]) → segList3
  50. Segment(PointListAxis2(13) + (0, 0.5), PointListAxis2(13) + (0, 0.4)) → arrow080
  51. CircleArc(Midpoint[PointListAxis2(14), PointListAxis2(13)] + (0, 0.5), PointListAxis2(14) + (0, 0.5), PointListAxis2(13) + (0, 0.5)) → arc081
  52. Text("$\textsf{\(-10\)}$", PointListAxis2(11 - 10) + (-0.155, (-segLength)), false, true, 0, -1) → txtM10
  53. Text("$\textsf{\(-9\)}$", PointListAxis2(11 - 9) + (-0.155, (-segLength)), false, true, 0, -1) → txtM9
  54. Text("$\textsf{\(-8\)}$", PointListAxis2(11 - 8) + (-0.155, (-segLength)), false, true, 0, -1) → txtM8
  55. Text("$\textsf{\(-7\)}$", PointListAxis2(11 - 7) + (-0.155, (-segLength)), false, true, 0, -1) → txtM7
  56. Text("$\textsf{\(-6\)}$", PointListAxis2(11 - 6) + (-0.155, (-segLength)), false, true, 0, -1) → txtM6
  57. Text("$\textsf{\(-5\)}$", PointListAxis2(11 - 5) + (-0.155, (-segLength)), false, true, 0, -1) → txtM5
  58. Text("$\textsf{\(-4\)}$", PointListAxis2(11 - 4) + (-0.155, (-segLength)), false, true, 0, -1) → txtM4
  59. Text("$\textsf{\(-3\)}$", PointListAxis2(11 - 3) + (-0.155, (-segLength)), false, true, 0, -1) → txtM3
  60. Text("$\textsf{\(-2\)}$", PointListAxis2(11 - 2) + (-0.155, (-segLength)), false, true, 0, -1) → txtM2
  61. Text("$\textsf{\(-1\)}$", PointListAxis2(11 - 1) + (-0.155, (-segLength)), false, true, 0, -1) → txtM1
  62. Text("$\textsf{0}$", PointListAxis2(11) + (0, (-segLength)), false, true, 0, -1) → txtP0
  63. Text("$\textsf{1}$", PointListAxis2(12) + (0, (-segLength)), false, true, 0, -1) → txtP1
  64. Text("$\textsf{2}$", PointListAxis2(13) + (0, (-segLength)), false, true, 0, -1) → txtP2
  65. Text("$\textsf{3}$", PointListAxis2(14) + (0, (-segLength)), false, true, 0, -1) → txtP3
  66. Text("$\textsf{4}$", PointListAxis2(15) + (0, (-segLength)), false, true, 0, -1) → txtP4
  67. Text("$\textsf{5}$", PointListAxis2(16) + (0, (-segLength)), false, true, 0, -1) → txtP5
  68. Text("$\textsf{6}$", PointListAxis2(17) + (0, (-segLength)), false, true, 0, -1) → txtP6
  69. Text("$\textsf{7}$", PointListAxis2(18) + (0, (-segLength)), false, true, 0, -1) → txtP7
  70. Text("$\textsf{8}$", PointListAxis2(19) + (0, (-segLength)), false, true, 0, -1) → txtP8
  71. Text("$\textsf{9}$", PointListAxis2(20) + (0, (-segLength)), false, true, 0, -1) → txtP9
  72. Text("$\textsf{10}$", PointListAxis2(21) + (0, (-segLength)), false, true, 0, -1) → txtP10
  73. Segment(PointListAxis3(1) + (0, (-If[1 ≟ 1, segLength0, segLength])), PointListAxis3(1) + (0, If[1 ≟ 1, segLength0, segLength])) → segP0
  74. Segment(PointListAxis3(2) + (0, (-segLength)), PointListAxis3(2) + (0, segLength)) → segP1
  75. Segment(PointListAxis3(3) + (0, (-segLength)), PointListAxis3(3) + (0, segLength)) → segP2
  76. Segment(PointListAxis3(4) + (0, (-segLength)), PointListAxis3(4) + (0, segLength)) → segP3
  77. Segment(PointListAxis3(5) + (0, (-segLength)), PointListAxis3(5) + (0, segLength)) → segP4
  78. Segment(PointListAxis3(6) + (0, (-segLength)), PointListAxis3(6) + (0, segLength)) → segP5
  79. Segment(PointListAxis3(7) + (0, (-segLength)), PointListAxis3(7) + (0, segLength)) → segP6
  80. Segment(PointListAxis3(8) + (0, (-segLength)), PointListAxis3(8) + (0, segLength)) → segP7
  81. Segment(PointListAxis3(9) + (0, (-segLength)), PointListAxis3(9) + (0, segLength)) → segP8
  82. Segment(PointListAxis3(10) + (0, (-segLength)), PointListAxis3(10) + (0, segLength)) → segP9
  83. Segment(PointListAxis3(11) + (0, (-segLength)), PointListAxis3(11) + (0, segLength)) → segP10
  84. Segment(PointListAxis2(1) + (0, (-segLength)), PointListAxis2(1) + (0, segLength)) → segM10
  85. Segment(PointListAxis2(2) + (0, (-segLength)), PointListAxis2(2) + (0, segLength)) → segM9
  86. Segment(PointListAxis2(3) + (0, (-segLength)), PointListAxis2(3) + (0, segLength)) → segM8
  87. Segment(PointListAxis2(4) + (0, (-segLength)), PointListAxis2(4) + (0, segLength)) → segM7
  88. Segment(PointListAxis2(5) + (0, (-segLength)), PointListAxis2(5) + (0, segLength)) → segM6
  89. Segment(PointListAxis2(6) + (0, (-segLength)), PointListAxis2(6) + (0, segLength)) → segM5
  90. Segment(PointListAxis2(7) + (0, (-segLength)), PointListAxis2(7) + (0, segLength)) → segM4
  91. Segment(PointListAxis2(8) + (0, (-segLength)), PointListAxis2(8) + (0, segLength)) → segM3
  92. Segment(PointListAxis2(9) + (0, (-segLength)), PointListAxis2(9) + (0, segLength)) → segM2
  93. Segment(PointListAxis2(10) + (0, (-segLength)), PointListAxis2(10) + (0, segLength)) → segM1
  94. PolyLine(PosSB, Corner[txt021, 4] + (-0.1, -0.1), Corner[txt021, 4] + (-0.1, 0.1), Corner[txt021, 3] + (0, 0.1), Corner[txt021, 2] + (0, -0.05), Corner[txt021, 1] + (-0.1, -0.05), Corner[txt021, 4] + (-0.1, -0.45), PosSB) → sb02
  95. PolyLine(PosSB, Corner[txt031, 4] + (-0.1, -0.1), Corner[txt031, 4] + (-0.1, 0.1), Corner[txt031, 3] + (0, 0.1), Corner[txt031, 2] + (0, -0.05), Corner[txt031, 1] + (-0.1, -0.05), Corner[txt031, 4] + (-0.1, -0.45), PosSB) → sb03
  96. Segment(Origin2 + (0, -0.9), Origin2 + (0, -1.2)) → segShowZ2
  97. Text("\textsf{Null}", Point[segShowZ2, 1], false, true, 0, -1) → txtShowZ2
  98. PolyLine(PosSB, Corner[txt051, 4] + (-0.1, 0.1 - 0.25), Corner[txt051, 4] + (-0.1, 0.1), Corner[txt051, 3] + (0.1, 0.1), Corner[txt051, 2] + (0.1, -0.05), Corner[txt051, 1] + (-0.1, -0.05), Corner[txt051, 4] + (-0.1, -1), PosSB) → sb05
  99. PolyLine(PosSB, Corner[txt061, 4] + (-0.1, 0.1 - 0.25), Corner[txt061, 4] + (-0.1, 0.1), Corner[txt061, 3] + (0.05, 0.1), Corner[txt061, 2] + (0.05, 0.05), Corner[txt061, 1] + (-0.1, 0.05), Corner[txt061, 4] + (-0.1, -1), PosSB) → sb06
  100. PolyLine(PosSB, Corner[txt071, 4] + (-0.1, -0.1), Corner[txt071, 4] + (-0.1, 0.1), Corner[txt071, 3] + (0, 0.1), Corner[txt071, 2] + (0, -0.05), Corner[txt071, 1] + (-0.1, -0.05), Corner[txt071, 4] + (-0.1, -0.45), PosSB) → sb07
  101. PolyLine(PosSB, Corner[txt081, 4] + (-0.1, -0.1), Corner[txt081, 4] + (-0.1, 0.1), Corner[txt081, 3] + (0, 0.1), Corner[txt081, 2] + (0, -0.05), Corner[txt081, 1] + (-0.1, -0.05), Corner[txt081, 4] + (-0.1, -0.45), PosSB) → sb09
  102. PolyLine(PosSB, Corner[txt081, 4] + (-0.1, 0.1 - 0.4), Corner[txt081, 4] + (-0.1, 0.1), Corner[txt081, 3] + (0, 0.1), Corner[txt081, 2] + (0, 0.05), Corner[txt081, 1] + (-0.1, 0.05), Corner[txt081, 4] + (-0.1, -0.75), PosSB) → sb08
  103. PolyLine(PosSB, Corner[txt101, 4] + (-0.1, 0.1 - 0.4), Corner[txt101, 4] + (-0.1, 0.1), Corner[txt101, 3] + (0, 0.1), Corner[txt101, 2] + (0, 0.05), Corner[txt101, 1] + (-0.1, 0.05), Corner[txt101, 4] + (-0.1, -0.75), PosSB) → sb10
  104. If(step ≟ 10, PosMonster1 + (0.3, -5.75), step ≟ 3, PosMonster1 + (0.25, -5.75), PosMonster1 + (0.25, -1.5)) → PosDouble
  105. If(step ≟ 5, bewegung ≟ 0 ∨ bewegung ≟ 1, step ≟ 2.5, anim3 ≟ 0 ∨ anim3 ≟ 3, true) → clickableBtnBack
  106. PolyLine(PosSB2, Corner[txt111, 4] + (-0.1, -0.3), Corner[txt111, 4] + (-0.1, 0.1), Corner[txt111, 3] + (0, 0.1), Corner[txt111, 2] + (0, -0.05), Corner[txt111, 1] + (-0.1, -0.05), Corner[txt111, 4] + (-0.1, -1), PosSB2) → sb11
  107. PolyLine(PosSB2, Corner[txt011, 4] + (-0.1, 0.1 - 0.25), Corner[txt011, 4] + (-0.1, 0.1), Corner[txt011, 3] + (0, 0.1), Corner[txt011, 2] + (0, 0.05), Corner[txt011, 1] + (-0.1, 0.05), Corner[txt011, 4] + (-0.1, -1), PosSB2) → sb01

AI 绘图提示语参考

绘制一个整数教学互动界面，包含三条水平数轴：上方数轴从0到10，中间数轴从-10到10，下方数轴从0到10，每条数轴带有刻度标签和垂直短线。在中间数轴上，用半圆弧和箭头标记两个区间，分别指向数字-2和7附近。界面中分布多个输入框、下拉菜单、按钮和反馈气泡，用于学生输入答案和查看提示。整体布局清晰，适合小学高年级学生理解整数比较与排序。
以上提示语为根据原始绘图命令整理而来，仅供参考。