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Set of Integers

Set of Integers
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2024-05-23 18:24
FunctionSequenceCoordinate GeometryGeometric ConstructionSlider Animation
In collections Ganze Zahlen & Arbeiten mit der Zahlengerade
This example demonstrates how to use GeoGebra to explore the concept of the set of integers. The core math concepts involved include the definition of integers, their representation on the number line, and the comparison and ordering of integers. Construction highlights - based on the 'Construction Summary' below, which GeoGebra commands/objects were used: Sequence, Element, Textfield, SpeechBubbleLeft, If, Segment, RemoveUndefined, SelectedIndex, CircleArc, Text, PolyLine; Objects: 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. Intended for: 5-6th grade students, to teach them how to use the number line to compare and order integers, and to interpret integers in mathematical and real-world situations.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Create an interactive integer learning interface with three horizontal number lines: the top one from 0 to 10, the middle from -10 to 10, and the bottom from 0 to 10, each with tick marks and labels. On the middle line, use semicircular arcs with arrows to highlight intervals near -2 and 7. Scatter several input boxes, dropdown menus, buttons, and speech bubbles across the canvas for student responses and feedback. The layout is clean and suitable for upper elementary students to grasp integer comparison and ordering.
The prompt above was compiled from the original drawing commands and is for reference only.