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A Fraction of a Set of Objects

A Fraction of a Set of Objects
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2022-03-17 11:37
FunctionSequenceCoordinate Geometry
This example helps students understand the concept of fractions by calculating a fraction of a set of objects. Key mathematical concepts include fractions and sets. It utilizes commands such as DynamicCoordinates, DivisorsList, Factors, Sequence, Polygon, Element, If, and Textfield in GeoGebra. Suitable for upper elementary or lower middle school students to learn about fractions and their applications.

GeoGebra Commands & Parameters

  1. DynamicCoordinates(P0, If[x(P0) < 2, 2, If[x(P0) > 12, 12, round(x(P0))]], If[y(P0) > -1, -1, If[y(P0) < -6, -6, round(y(P0))]]) → P
  2. DivisorsList(n) → nfactors
  3. Factors(n) →
  4. DivisorsList(m) → mfactors
  5. Factors(m) →
  6. Sequence(Segment[((i * m / Element[mfactors, mdiv]), 0), ((i * m / Element[mfactors, mdiv]), (-n))], i, 1, Element[mfactors, mdiv] - 1) → l2
  7. Sequence(Segment[(0, ((-i) * n / Element[nfactors, ndiv])), (m, ((-i) * n / Element[nfactors, ndiv]))], i, 1, Element[nfactors, ndiv] - 1) → l3
  8. Polygon({(b - b, 0), (b, 0), (b, (-h)), (b - b, (-h))}) → q101
  9. Polygon({((2 * b) - b, 0), ((2 * b), 0), ((2 * b), (-h)), ((2 * b) - b, (-h))}) → q102
  10. Polygon({((3 * b) - b, 0), ((3 * b), 0), ((3 * b), (-h)), ((3 * b) - b, (-h))}) → q103
  11. Polygon({((4 * b) - b, 0), ((4 * b), 0), ((4 * b), (-h)), ((4 * b) - b, (-h))}) → q104
  12. Polygon({((5 * b) - b, 0), ((5 * b), 0), ((5 * b), (-h)), ((5 * b) - b, (-h))}) → q105
  13. Polygon({((6 * b) - b, 0), ((6 * b), 0), ((6 * b), (-h)), ((6 * b) - b, (-h))}) → q106
  14. Polygon({((7 * b) - b, 0), ((7 * b), 0), ((7 * b), (-h)), ((7 * b) - b, (-h))}) → q107
  15. Polygon({((8 * b) - b, 0), ((8 * b), 0), ((8 * b), (-h)), ((8 * b) - b, (-h))}) → q108
  16. Polygon({((9 * b) - b, 0), ((9 * b), 0), ((9 * b), (-h)), ((9 * b) - b, (-h))}) → q109
  17. Polygon({(b - b, (-h)), (b, (-h)), (b, (-2 * h)), (b - b, (-2 * h))}) → q201
  18. Polygon({((2 * b) - b, (-h)), ((2 * b), (-h)), ((2 * b), (-2 * h)), ((2 * b) - b, (-2 * h))}) → q202
  19. Polygon({((3 * b) - b, (-h)), ((3 * b), (-h)), ((3 * b), (-2 * h)), ((3 * b) - b, (-2 * h))}) → q203
  20. Polygon({((4 * b) - b, (-h)), ((4 * b), (-h)), ((4 * b), (-2 * h)), ((4 * b) - b, (-2 * h))}) → q204
  21. Polygon({((5 * b) - b, (-h)), ((5 * b), (-h)), ((5 * b), (-2 * h)), ((5 * b) - b, (-2 * h))}) → q205
  22. Polygon({((6 * b) - b, (-h)), ((6 * b), (-h)), ((6 * b), (-2 * h)), ((6 * b) - b, (-2 * h))}) → q206
  23. Polygon({((7 * b) - b, (-h)), ((7 * b), (-h)), ((7 * b), (-2 * h)), ((7 * b) - b, (-2 * h))}) → q207
  24. Polygon({((8 * b) - b, (-h)), ((8 * b), (-h)), ((8 * b), (-2 * h)), ((8 * b) - b, (-2 * h))}) → q208
  25. Polygon({((9 * b) - b, (-h)), ((9 * b), (-h)), ((9 * b), (-2 * h)), ((9 * b) - b, (-2 * h))}) → q209
  26. Polygon({(b - b, (-2 * h)), (b, (-2 * h)), (b, (-3 * h)), (b - b, (-3 * h))}) → q301
  27. Polygon({((2 * b) - b, (-2 * h)), ((2 * b), (-2 * h)), ((2 * b), (-3 * h)), ((2 * b) - b, (-3 * h))}) → q302
  28. Polygon({((3 * b) - b, (-2 * h)), ((3 * b), (-2 * h)), ((3 * b), (-3 * h)), ((3 * b) - b, (-3 * h))}) → q303
  29. Polygon({((4 * b) - b, (-2 * h)), ((4 * b), (-2 * h)), ((4 * b), (-3 * h)), ((4 * b) - b, (-3 * h))}) → q304
  30. Polygon({((5 * b) - b, (-2 * h)), ((5 * b), (-2 * h)), ((5 * b), (-3 * h)), ((5 * b) - b, (-3 * h))}) → q305
  31. Polygon({((6 * b) - b, (-2 * h)), ((6 * b), (-2 * h)), ((6 * b), (-3 * h)), ((6 * b) - b, (-3 * h))}) → q306
  32. Polygon({((7 * b) - b, (-2 * h)), ((7 * b), (-2 * h)), ((7 * b), (-3 * h)), ((7 * b) - b, (-3 * h))}) → q307
  33. Polygon({((8 * b) - b, (-2 * h)), ((8 * b), (-2 * h)), ((8 * b), (-3 * h)), ((8 * b) - b, (-3 * h))}) → q308
  34. Polygon({((9 * b) - b, (-2 * h)), ((9 * b), (-2 * h)), ((9 * b), (-3 * h)), ((9 * b) - b, (-3 * h))}) → q309
  35. Polygon({(b - b, (-3 * h)), (b, (-3 * h)), (b, (-4 * h)), (b - b, (-4 * h))}) → q401
  36. Polygon({((2 * b) - b, (-3 * h)), ((2 * b), (-3 * h)), ((2 * b), (-4 * h)), ((2 * b) - b, (-4 * h))}) → q402
  37. Polygon({((3 * b) - b, (-3 * h)), ((3 * b), (-3 * h)), ((3 * b), (-4 * h)), ((3 * b) - b, (-4 * h))}) → q403
  38. Polygon({((4 * b) - b, (-3 * h)), ((4 * b), (-3 * h)), ((4 * b), (-4 * h)), ((4 * b) - b, (-4 * h))}) → q404
  39. Polygon({((5 * b) - b, (-3 * h)), ((5 * b), (-3 * h)), ((5 * b), (-4 * h)), ((5 * b) - b, (-4 * h))}) → q405
  40. Polygon({((6 * b) - b, (-3 * h)), ((6 * b), (-3 * h)), ((6 * b), (-4 * h)), ((6 * b) - b, (-4 * h))}) → q406
  41. Polygon({((7 * b) - b, (-3 * h)), ((7 * b), (-3 * h)), ((7 * b), (-4 * h)), ((7 * b) - b, (-4 * h))}) → q407
  42. Polygon({((8 * b) - b, (-3 * h)), ((8 * b), (-3 * h)), ((8 * b), (-4 * h)), ((8 * b) - b, (-4 * h))}) → q408
  43. Polygon({((9 * b) - b, (-3 * h)), ((9 * b), (-3 * h)), ((9 * b), (-4 * h)), ((9 * b) - b, (-4 * h))}) → q409
  44. Polygon({(b - b, (-4 * h)), (b, (-4 * h)), (b, (-5 * h)), (b - b, (-5 * h))}) → q501
  45. Polygon({((2 * b) - b, (-4 * h)), ((2 * b), (-4 * h)), ((2 * b), (-5 * h)), ((2 * b) - b, (-5 * h))}) → q502
  46. Polygon({((3 * b) - b, (-4 * h)), ((3 * b), (-4 * h)), ((3 * b), (-5 * h)), ((3 * b) - b, (-5 * h))}) → q503
  47. Polygon({((4 * b) - b, (-4 * h)), ((4 * b), (-4 * h)), ((4 * b), (-5 * h)), ((4 * b) - b, (-5 * h))}) → q504
  48. Polygon({((5 * b) - b, (-4 * h)), ((5 * b), (-4 * h)), ((5 * b), (-5 * h)), ((5 * b) - b, (-5 * h))}) → q505
  49. Polygon({((6 * b) - b, (-4 * h)), ((6 * b), (-4 * h)), ((6 * b), (-5 * h)), ((6 * b) - b, (-5 * h))}) → q506
  50. Polygon({((7 * b) - b, (-4 * h)), ((7 * b), (-4 * h)), ((7 * b), (-5 * h)), ((7 * b) - b, (-5 * h))}) → q507
  51. Polygon({((8 * b) - b, (-4 * h)), ((8 * b), (-4 * h)), ((8 * b), (-5 * h)), ((8 * b) - b, (-5 * h))}) → q508
  52. Polygon({((9 * b) - b, (-4 * h)), ((9 * b), (-4 * h)), ((9 * b), (-5 * h)), ((9 * b) - b, (-5 * h))}) → q509
  53. Polygon({(b - b, (-5 * h)), (b, (-5 * h)), (b, (-6 * h)), (b - b, (-6 * h))}) → q601
  54. Polygon({((2 * b) - b, (-5 * h)), ((2 * b), (-5 * h)), ((2 * b), (-6 * h)), ((2 * b) - b, (-6 * h))}) → q602
  55. Polygon({((3 * b) - b, (-5 * h)), ((3 * b), (-5 * h)), ((3 * b), (-6 * h)), ((3 * b) - b, (-6 * h))}) → q603
  56. Polygon({((4 * b) - b, (-5 * h)), ((4 * b), (-5 * h)), ((4 * b), (-6 * h)), ((4 * b) - b, (-6 * h))}) → q604
  57. Polygon({((5 * b) - b, (-5 * h)), ((5 * b), (-5 * h)), ((5 * b), (-6 * h)), ((5 * b) - b, (-6 * h))}) → q605
  58. Polygon({((6 * b) - b, (-5 * h)), ((6 * b), (-5 * h)), ((6 * b), (-6 * h)), ((6 * b) - b, (-6 * h))}) → q606
  59. Polygon({((7 * b) - b, (-5 * h)), ((7 * b), (-5 * h)), ((7 * b), (-6 * h)), ((7 * b) - b, (-6 * h))}) → q607
  60. Polygon({((8 * b) - b, (-5 * h)), ((8 * b), (-5 * h)), ((8 * b), (-6 * h)), ((8 * b) - b, (-6 * h))}) → q608
  61. Polygon({((9 * b) - b, (-5 * h)), ((9 * b), (-5 * h)), ((9 * b), (-6 * h)), ((9 * b) - b, (-6 * h))}) → q609
  62. Polygon({((10 * b) - b, 0), ((10 * b), 0), ((10 * b), (-h)), ((10 * b) - b, (-h))}) → q110
  63. Polygon({((11 * b) - b, 0), ((11 * b), 0), ((11 * b), (-h)), ((11 * b) - b, (-h))}) → q111
  64. Polygon({((12 * b) - b, 0), ((12 * b), 0), ((12 * b), (-h)), ((12 * b) - b, (-h))}) → q112
  65. Polygon({((10 * b) - b, (-h)), ((10 * b), (-h)), ((10 * b), (-2 * h)), ((10 * b) - b, (-2 * h))}) → q210
  66. Polygon({((11 * b) - b, (-h)), ((11 * b), (-h)), ((11 * b), (-2 * h)), ((11 * b) - b, (-2 * h))}) → q211
  67. Polygon({((12 * b) - b, (-h)), ((12 * b), (-h)), ((12 * b), (-2 * h)), ((12 * b) - b, (-2 * h))}) → q212
  68. Polygon({((10 * b) - b, (-2 * h)), ((10 * b), (-2 * h)), ((10 * b), (-3 * h)), ((10 * b) - b, (-3 * h))}) → q310
  69. Polygon({((11 * b) - b, (-2 * h)), ((11 * b), (-2 * h)), ((11 * b), (-3 * h)), ((11 * b) - b, (-3 * h))}) → q311
  70. Polygon({((12 * b) - b, (-2 * h)), ((12 * b), (-2 * h)), ((12 * b), (-3 * h)), ((12 * b) - b, (-3 * h))}) → q312
  71. Polygon({((10 * b) - b, (-3 * h)), ((10 * b), (-3 * h)), ((10 * b), (-4 * h)), ((10 * b) - b, (-4 * h))}) → q410
  72. Polygon({((11 * b) - b, (-3 * h)), ((11 * b), (-3 * h)), ((11 * b), (-4 * h)), ((11 * b) - b, (-4 * h))}) → q411
  73. Polygon({((12 * b) - b, (-3 * h)), ((12 * b), (-3 * h)), ((12 * b), (-4 * h)), ((12 * b) - b, (-4 * h))}) → q412
  74. Polygon({((10 * b) - b, (-4 * h)), ((10 * b), (-4 * h)), ((10 * b), (-5 * h)), ((10 * b) - b, (-5 * h))}) → q510
  75. Polygon({((11 * b) - b, (-4 * h)), ((11 * b), (-4 * h)), ((11 * b), (-5 * h)), ((11 * b) - b, (-5 * h))}) → q511
  76. Polygon({((12 * b) - b, (-4 * h)), ((12 * b), (-4 * h)), ((12 * b), (-5 * h)), ((12 * b) - b, (-5 * h))}) → q512
  77. Polygon({((10 * b) - b, (-5 * h)), ((10 * b), (-5 * h)), ((10 * b), (-6 * h)), ((10 * b) - b, (-6 * h))}) → q610
  78. Polygon({((11 * b) - b, (-5 * h)), ((11 * b), (-5 * h)), ((11 * b), (-6 * h)), ((11 * b) - b, (-6 * h))}) → q611
  79. Polygon({((12 * b) - b, (-5 * h)), ((12 * b), (-5 * h)), ((12 * b), (-6 * h)), ((12 * b) - b, (-6 * h))}) → q612
  80. Element(mfactors, mdiv) → numcolumns
  81. Element(nfactors, ndiv) → numrows
  82. Polygon({(0, 0), (x(P), 0), P, (0, y(P))}) → q1
  83. If(response1 ≟ "", false, true) → input1
  84. If(response2 ≟ "", false, true) → input2
  85. If(response1 ≟ ans1, true, false) → correct1
  86. If(response2 ≟ ans2, true, false) → correct2
  87. Textfield(response2) → InputBox2
  88. Textfield(response1) → InputBox1
  89. DynamicCoordinates(P0_{1}, If[x(P0_{1}) < 2, 2, If[x(P0_{1}) > 12, 12, round(x(P0_{1}))]], If[y(P0_{1}) > -1, -1, If[y(P0_{1}) < -6, -6, round(y(P0_{1}))]]) → P_{1}
  90. DivisorsList(n_{1}) → nfactors_{1}
  91. Factors(n_{1}) →
  92. DivisorsList(m_{1}) → mfactors_{1}
  93. Factors(m_{1}) →
  94. Sequence(Translate[pic1, (i - 1, -1)], i, 1, m) → l1
  95. Sequence(Translate[l1, (0, (-j) + 1)], j, 1, n) → m1

AI Drawing Prompt Reference

Draw a coordinate system with a dynamic point near the origin, whose x and y coordinates are constrained between 2 and 12 and -1 and -6, respectively. Based on a number n, draw horizontal line segments for each of its divisors, extending downward from the x-axis at corresponding positions. Based on another number m, draw vertical line segments for each of its divisors, extending rightward from the y-axis at corresponding positions. On the x-axis, draw 10 rectangles from b to 9b, each with height h. Below the y-axis, draw 10 rectangles from -2h to -5h, each with width b. All rectangles are aligned parallel to the x-axis or y-axis.
The prompt above was compiled from the original drawing commands and is for reference only.