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Multiplication and Division in Card Games

Multiplication and Division in Card Games
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2024-07-03 21:39
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This example demonstrates how to use card games to illustrate the concepts of multiplication and division. Students can understand the relationship between multiplication and division by swapping numbers. For example, 7 × 4 = 28 can be understood as 28 ÷ 4 = 7 or 28 ÷ 7 = 4. This example uses GeoGebra to create an interactive card game where students can click buttons to change numbers and observe the relationship between multiplication and division. This example is suitable for elementary and middle school mathematics education, particularly for understanding the relationship between multiplication and division.

GeoGebra Commands & Parameters

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {3, 1, 4, 4, 3, 8, 5, 2, 2, 5}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. RemoveUndefined({"$\textsf{\phantom{2 }}$", "$\textsf{2 }$", "$\textsf{3 }$", "$\textsf{4 }$", "$\textsf{6 }$", If[step < 9, "$\textsf{8 }$"]}) → dropdown021
  5. If(SelectedIndex[dropdown021] ≟ 1, 0, 8, SelectedIndex[dropdown021] ≟ 2, 2, SelectedIndex[dropdown021] ≟ 3, 3, SelectedIndex[dropdown021] ≟ 4, 4, SelectedIndex[dropdown021] ≟ 5, 6) → anzahlP
  6. If(step < 9, 24, (4 * anzahlP)) → anzahlK
  7. Text((("\textsf{Anzahl Spielkarten: " * anzahlK) * "}"), Ausrichtung, false, true, 0, -1) → txt022
  8. Corner(imgK1, 3) → PosImgKarte013
  9. Sequence(Translate[imgK1, Vector[(k * (dimK + disK, 0))]], k, 1, anzahlK / 2 - 1) → KartenReihe1
  10. Sequence(Translate[Element[Join[{{imgK1}, KartenReihe1}], k], PosImgKarte012 - PosImgKarte013 - (0, disK)], k, 1, anzahlK / 2) → KartenReihe2
  11. If(anzahlP ≟ 2, 5, anzahlP ≟ 3, 2.5, anzahlP ≟ 4, If[step ≥ 9, 2.2, 1.6], anzahlP ≟ 6, 2.4, 1.5) → disP
  12. Join({{imgKG1}, Sequence[Translate[imgKG1, Vector[(k * (dimK + disK, 0))]], k, 1, anzahlK / 2 - 1]}) → KGReihe1
  13. If(anzahlP ≠ 0, anzahlK / anzahlP, 1) → anzahlKpP
  14. Translate(imgK1, Vector[PosImgKarte011, PosKP1]) → imgKP1
  15. Translate(imgK1, Vector[PosImgKarte011, PosKP2]) → imgKP2
  16. Translate(imgK1, Vector[PosImgKarte011, PosKP3]) → imgKP3
  17. Translate(imgK1, Vector[PosImgKarte011, PosKP6]) → imgKP6
  18. Translate(imgK1, Vector[PosImgKarte011, PosKP7]) → imgKP7
  19. Translate(imgK1, Vector[PosImgKarte011, PosKP8]) → imgKP8
  20. Translate(imgK1, Vector[PosImgKarte011, PosKP4]) → imgKP4
  21. Translate(imgK1, Vector[PosImgKarte011, PosKP5]) → imgKP5
  22. Sequence(Translate[imgKP1, Vector[(k * (disK + dimK, 0))]], k, 0, anzahlKpP / If[anzahlKpP > 4, 2, 1] - 1) → KR11
  23. Sequence(Translate[imgKP2, Vector[(k * (disK + dimK, 0))]], k, 0, anzahlKpP / If[anzahlKpP > 4, 2, 1] - 1) → KR21
  24. Sequence(Translate[imgKP3, Vector[(k * (disK + dimK, 0))]], k, 0, anzahlKpP / If[anzahlKpP > 4, 2, 1] - 1) → KR31
  25. Sequence(Translate[imgKP4, Vector[(k * (disK + dimK, 0))]], k, 0, anzahlKpP / If[anzahlKpP > 4, 2, 1] - 1) → KR41
  26. Sequence(Translate[Element[KR11, k], Vector[(0, (-disK) - (1.463 * dimK))]], k, 1, Length[KR11]) → KR12
  27. Sequence(Translate[Element[KR21, k], Vector[(0, (-disK) - (1.463 * dimK))]], k, 1, Length[KR11]) → KR22
  28. Sequence(Translate[Element[KR31, k], Vector[(0, (-disK) - (1.463 * dimK))]], k, 1, Length[KR11]) → KR32
  29. Sequence(Translate[Element[KR41, k], Vector[(0, (-disK) - (1.463 * dimK))]], k, 1, Length[KR11]) → KR42
  30. Sequence(Translate[imgKP5, Vector[(k * (disK + dimK, 0))]], k, 0, anzahlKpP / If[anzahlKpP > 4, 2, 1] - 1) → KR51
  31. Sequence(Translate[imgKP6, Vector[(k * (disK + dimK, 0))]], k, 0, anzahlKpP / If[anzahlKpP > 4, 2, 1] - 1) → KR61
  32. Sequence(Translate[imgKP7, Vector[(k * (disK + dimK, 0))]], k, 0, anzahlKpP / If[anzahlKpP > 4, 2, 1] - 1) → KR71
  33. Sequence(Translate[imgKP8, Vector[(k * (disK + dimK, 0))]], k, 0, anzahlKpP / If[anzahlKpP > 4, 2, 1] - 1) → KR81
  34. Text((("\textsf{Spielkarten pro Kind: " * If[step ≥ 9, 4, anzahlKpP]) * "}"), (x(Ausrichtung), y(If[anzahlP ∈ {2, 3, 4} ∧ step < 9 ∨ anzahlP ∈ {2, 3} ∧ step ≥ 9, PosP11 - ((2 * 1.463) * dimK) - (3 * disK), PosP51 - (1.463 * dimK) - (2 * disK)])), false, true, 0, -1) → txt031
  35. CircleArc(Midpoint[Ausrichtung, (x(Ausrichtung), y(If[anzahlKpP ∈ {12, 8, 6}, PosP11 - ((2 * 1.463) * dimK) - (3 * disK), PosP51 - (1.463 * dimK) - (2 * disK)]))] + (-3, 0), Midpoint[Corner[txt031, 2], Corner[txt031, 3]] + (3.9, 0.5), Midpoint[Corner[txt022, 2], Corner[txt022, 3]] + (3.1, -0.9)) → arc041
  36. Line(Ausrichtung, Pos1) → sym
  37. Mirror(arc041, sym) → arc071
  38. Segment(Point[arc041, 0], Point[arc041, 0] + (0.25 * UnitVector[Tangent[Point[arc041, 0], arc041]])) → seg041
  39. Segment(Point[arc071, 1], Point[arc071, 1] + (0.25 * UnitVector[Tangent[Point[arc071, 1], arc071]])) → seg071
  40. Sequence(Translate[Element[KGReihe1, k], PosImgKarte012 - PosImgKarte013 - (0, disK)], k, 1, anzahlK / 2) → KGReihe2
  41. Mirror(PosArc041, sym) → PosArc071
  42. Textfield(input041) → InputBox041
  43. Textfield(input071) → InputBox071
  44. Textfield(input101) → InputBox101
  45. Textfield(input121) → InputBox121
  46. Invert(pixMat) → invPixMat
  47. CircleArc(Midpoint[PosArc11, PosArc12] + (1.5 * UnitOrthogonalVector[Segment[PosArc12, PosArc11]]), PosArc12, PosArc11) → arc1
  48. Sequence(Translate[Translate[imgKG1, Vector[Corner[imgKG1, 1], PosKP1]], Vector[(k * (disK + dimK, 0))]], k, 0, anzahlKpP / If[anzahlKpP > 4, 2, 1] - 1) → KGR11
  49. Sequence(Translate[Element[KGR11, k], Vector[(0, (-disK) - (1.463 * dimK))]], k, 1, Length[KGR11]) → KGR12
  50. Sequence(Translate[Translate[imgKG1, Vector[Corner[imgKG1, 1], PosKP2]], Vector[(k * (disK + dimK, 0))]], k, 0, anzahlKpP / If[anzahlKpP > 4, 2, 1] - 1) → KGR21
  51. Sequence(Translate[Translate[imgKG1, Vector[Corner[imgKG1, 1], PosKP3]], Vector[(k * (disK + dimK, 0))]], k, 0, anzahlKpP / If[anzahlKpP > 4, 2, 1] - 1) → KGR31
  52. Sequence(Translate[Translate[imgKG1, Vector[Corner[imgKG1, 1], PosKP4]], Vector[(k * (disK + dimK, 0))]], k, 0, anzahlKpP / If[anzahlKpP > 4, 2, 1] - 1) → KGR41
  53. Sequence(Translate[Translate[imgKG1, Vector[Corner[imgKG1, 1], PosKP5]], Vector[(k * (disK + dimK, 0))]], k, 0, anzahlKpP / If[anzahlKpP > 4, 2, 1] - 1) → KGR51
  54. Sequence(Translate[Translate[imgKG1, Vector[Corner[imgKG1, 1], PosKP6]], Vector[(k * (disK + dimK, 0))]], k, 0, anzahlKpP / If[anzahlKpP > 4, 2, 1] - 1) → KGR61
  55. Sequence(Translate[Translate[imgKG1, Vector[Corner[imgKG1, 1], PosKP7]], Vector[(k * (disK + dimK, 0))]], k, 0, anzahlKpP / If[anzahlKpP > 4, 2, 1] - 1) → KGR71
  56. Sequence(Translate[Translate[imgKG1, Vector[Corner[imgKG1, 1], PosKP8]], Vector[(k * (disK + dimK, 0))]], k, 0, anzahlKpP / If[anzahlKpP > 4, 2, 1] - 1) → KGR81
  57. Sequence(Translate[Element[KGR21, k], Vector[(0, (-disK) - (1.463 * dimK))]], k, 1, Length[KGR21]) → KGR22
  58. Sequence(Translate[Element[KGR31, k], Vector[(0, (-disK) - (1.463 * dimK))]], k, 1, Length[KGR31]) → KGR32
  59. Sequence(Translate[Element[KGR41, k], Vector[(0, (-disK) - (1.463 * dimK))]], k, 1, Length[KGR41]) → KGR42
  60. Sequence(Translate[Element[KGR51, k], Vector[(0, (-disK) - (1.463 * dimK))]], k, 1, Length[KGR51]) → KGR52
  61. Sequence(Translate[Element[KGR61, k], Vector[(0, (-disK) - (1.463 * dimK))]], k, 1, Length[KGR61]) → KGR62
  62. If(step ≟ 4, correctdd041 ∧ correct041, step ≟ 7, correctdd071 ∧ correct071, step ≟ 10, correctdd101 ∧ correct101, step ≟ 12, correctdd121 ∧ correct121, true) → clickableBtnNext
  63. CircleArc(Midpoint[PosZ1, PosZ2] + (0, -2), PosZ2 + (-0.25, 0.5), PosZ1 + (0.25, 0.5)) → arc141
  64. CircleArc(Midpoint[PosZ1, PosZ2] + (0, 2), PosZ1 + (0.27, -0.6), PosZ2 + (-0.25, -0.5)) → arc142
  65. Vector(Point[arc141, 0], Point[arc141, 0] + (0.1, -0.1)) → vec141
  66. Vector(Point[arc142, 0], Point[arc142, 0] + (-0.1, 0.1)) → vec142
  67. Vector(Point[arc1, 0], Point[arc1, 0] + (0.1 * UnitVector[Tangent[Point[arc1, 0], arc1]])) → vec1
  68. CircleArc(Midpoint[PosArc21, PosArc22] - (1.5 * UnitOrthogonalVector[Segment[PosArc22, PosArc21]]), PosArc21, PosArc22) → arc2
  69. Vector(Point[arc2, 0], Point[arc2, 0] + (0.1 * UnitVector[Tangent[Point[arc2, 0], arc2]])) → vec2
  70. Ellipse(Midpoint[Corner[Element[KR31, 1], 1], Corner[Element[KR32, 1], 4]], Midpoint[Corner[Element[KR31, 4], 2], Corner[Element[KR32, 4], 3]], 2.1) → ell13
  71. Ellipse(Midpoint[Corner[Element[KR41, 1], 1], Corner[Element[KR42, 1], 4]], Midpoint[Corner[Element[KR41, 3], 2], Corner[Element[KR42, 3], 3]], 1.75) → ell14
  72. Ellipse(Midpoint[Corner[Element[KR41, 1], 1], Corner[Element[KR41, 1], 4]], Midpoint[Corner[Element[KR41, 4], 2], Corner[Element[KR41, 4], 3]], 1.8) → ell16
  73. Ellipse(Midpoint[Corner[Element[KR41, 1], 1], Corner[Element[KR41, 1], 4]], Midpoint[Corner[Element[KR41, 3], 2], Corner[Element[KR41, 3], 3]], 1.45) → ell18
  74. Ellipse(Midpoint[Corner[Element[KR21, 1], 1], Corner[Element[KR22, 1], 4]] - (0.45, 0), Midpoint[Corner[Element[KR21, 6], 2], Corner[Element[KR22, 6], 3]] + (0.45, 0), 3.25) → ell12
  75. Ellipse(Midpoint[Corner[Element[KR11, 1], 1], Corner[Element[KR12, 1], 4]] - (0.45, 0), Midpoint[Corner[Element[KR11, 6], 2], Corner[Element[KR12, 6], 3]] + (0.45, 0), 3.25) → ell22
  76. Ellipse(Midpoint[Corner[Element[KR11, 1], 1], Corner[Element[KR12, 1], 4]], Midpoint[Corner[Element[KR11, 4], 2], Corner[Element[KR12, 4], 3]], 2.1) → ell23
  77. Ellipse(Midpoint[Corner[Element[KR11, 1], 1], Corner[Element[KR12, 1], 4]], Midpoint[Corner[Element[KR11, 3], 2], Corner[Element[KR12, 3], 3]], 1.75) → ell24
  78. Ellipse(Midpoint[Corner[Element[KR11, 1], 1], Corner[Element[KR11, 1], 4]], Midpoint[Corner[Element[KR11, 4], 2], Corner[Element[KR11, 4], 3]], 1.8) → ell26
  79. Ellipse(Midpoint[Corner[Element[KR11, 1], 1], Corner[Element[KR11, 1], 4]], Midpoint[Corner[Element[KR11, 3], 2], Corner[Element[KR11, 3], 3]], 1.45) → ell28
  80. If(step ≟ 4, PosDD041 + (-0.15, -1), step ≟ 7, PosDD071 + (-0.5, -1), (1, 1)) → PosBtnShowSolution

AI Drawing Prompt Reference

Create an elementary math interactive teaching graphic showing multiplication and division relationships through a card game. At the top, a dropdown menu allows selecting numbers (2, 3, 4, 6, 8). When selected, corresponding card arrays display on the screen arranged neatly from left to right. Two lines of German text appear: the top shows total card quantity, the bottom shows cards per player. Arc lines connect between card arrays indicating the multiplication-division relationship. Four input boxes on the right side are for student answers. The layout is clear with simple card graphics on a light background.
The prompt above was compiled from the original drawing commands and is for reference only.