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Explore Equivalent Fractions by Juli Jurado i Llamas

Explore Equivalent Fractions by Juli Jurado i Llamas
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2016-07-19 00:38
PolygonTrigonometryGeometric Construction
This example demonstrates how to find equivalent fractions using GeoGebra. It involves the concept of fractions and explores the properties of equivalent fractions through the construction of parallelograms and medians. Commands used include Polygon, Sequence, Random, IndexOf, If, Segment, and Sum. Suitable for high-grade elementary or junior high school students to learn about the equivalence of fractions.

GeoGebra Commands & Parameters

  1. Polygon(A1, B1, 4) → Polígon1, a, b, c, d, A, B
  2. Polygon(A2, B2, 4) → Polígon2, e, f, g, h, C, D
  3. Polygon(A3, B3, 4) → Polígon3, i, j, k, l, E, F
  4. Polygon(A4, B4, 4) → Polígon4, m, n, p, q, G, H
  5. Sequence(Sample[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, 12, false], i, 1, 10) → matriu1
  6. Random(1, 10) → fila
  7. IndexOf(1, Element[matriu1, fila]) → E1
  8. IndexOf(2, Element[matriu1, fila]) → E2
  9. IndexOf(3, Element[matriu1, fila]) → E3
  10. IndexOf(4, Element[matriu1, fila]) → E4
  11. IndexOf(5, Element[matriu1, fila]) → E5
  12. IndexOf(6, Element[matriu1, fila]) → E6
  13. IndexOf(7, Element[matriu1, fila]) → E7
  14. IndexOf(8, Element[matriu1, fila]) → E8
  15. IndexOf(9, Element[matriu1, fila]) → E9
  16. IndexOf(10, Element[matriu1, fila]) → E10
  17. IndexOf(11, Element[matriu1, fila]) → E11
  18. IndexOf(12, Element[matriu1, fila]) → E12
  19. If(Mod[E1, 3] ≟ 1, E1 + 1, If[Mod[E1, 3] ≟ 2, E1 - 1, E1 - 2]) → F1
  20. If(Mod[E2, 3] ≟ 1, E2 + 1, If[Mod[E2, 3] ≟ 2, E2 - 1, E2 - 2]) → F2
  21. If(Mod[E3, 3] ≟ 1, E3 + 1, If[Mod[E3, 3] ≟ 2, E3 - 1, E3 - 2]) → F3
  22. If(Mod[E4, 3] ≟ 1, E4 + 1, If[Mod[E4, 3] ≟ 2, E4 - 1, E4 - 2]) → F4
  23. If(Mod[E5, 3] ≟ 1, E5 + 1, If[Mod[E5, 3] ≟ 2, E5 - 1, E5 - 2]) → F5
  24. If(Mod[E6, 3] ≟ 1, E6 + 1, If[Mod[E6, 3] ≟ 2, E6 - 1, E6 - 2]) → F6
  25. If(Mod[E7, 3] ≟ 1, E7 + 1, If[Mod[E7, 3] ≟ 2, E7 - 1, E7 - 2]) → F7
  26. If(Mod[E8, 3] ≟ 1, E8 + 1, If[Mod[E8, 3] ≟ 2, E8 - 1, E8 - 2]) → F8
  27. If(Mod[E9, 3] ≟ 1, E9 + 1, If[Mod[E9, 3] ≟ 2, E9 - 1, E9 - 2]) → F9
  28. If(Mod[E10, 3] ≟ 1, E10 + 1, If[Mod[E10, 3] ≟ 2, E10 - 1, E10 - 2]) → F10
  29. If(Mod[E11, 3] ≟ 1, E11 + 1, If[Mod[E11, 3] ≟ 2, E11 - 1, E11 - 2]) → F11
  30. If(Mod[E12, 3] ≟ 1, E12 + 1, If[Mod[E12, 3] ≟ 2, E12 - 1, E12 - 2]) → F12
  31. Polygon(A5, B5, 4) → Polígon5, r, s, t, a_1, I, J
  32. Polygon(A6, B6, 4) → Polígon6, b_1, c_1, d_1, e_1, K, L
  33. Polygon(A7, B7, 4) → Polígon7, f_1, g_1, h_1, i_1, N, O
  34. Polygon(A8, B8, 4) → Polígon8, j_1, k_1, l_1, m_1, R, S
  35. Polygon(A9, B9, 4) → Polígon9, n_1, p_1, q_1, r_1, T, U
  36. Polygon(A10, B10, 4) → Polígon10, s_1, t_1, a_2, b_2, V, W
  37. Polygon(A11, B11, 4) → Polígon11, c_2, d_2, e_2, f_2, Z, A_1
  38. Polygon(A12, B12, 4) → Polígon12, g_2, h_2, i_2, j_2, B_1, C_1
  39. IndexOf(10, Element[matriu1, fila]) → o
  40. If(Mod[E1, 3] ≟ 1, E1 + 2, If[Mod[E1, 3] ≟ 2, E1 + 1, E1 - 1]) → G1
  41. If(Mod[E2, 3] ≟ 1, E2 + 2, If[Mod[E2, 3] ≟ 2, E2 + 1, E2 - 1]) → G2
  42. If(Mod[E3, 3] ≟ 1, E3 + 2, If[Mod[E3, 3] ≟ 2, E3 + 1, E3 - 1]) → G3
  43. If(Mod[E4, 3] ≟ 1, E4 + 2, If[Mod[E4, 3] ≟ 2, E4 + 1, E4 - 1]) → G4
  44. If(Mod[E5, 3] ≟ 1, E5 + 2, If[Mod[E5, 3] ≟ 2, E5 + 1, E5 - 1]) → G5
  45. If(Mod[E6, 3] ≟ 1, E6 + 2, If[Mod[E6, 3] ≟ 2, E6 + 1, E6 - 1]) → G6
  46. If(Mod[E7, 3] ≟ 1, E7 + 2, If[Mod[E7, 3] ≟ 2, E7 + 1, E7 - 1]) → G7
  47. If(Mod[E8, 3] ≟ 1, E8 + 2, If[Mod[E8, 3] ≟ 2, E8 + 1, E8 - 1]) → G8
  48. If(Mod[E9, 3] ≟ 1, E9 + 2, If[Mod[E9, 3] ≟ 2, E9 + 1, E9 - 1]) → G9
  49. If(Mod[E10, 3] ≟ 1, E10 + 2, If[Mod[E10, 3] ≟ 2, E10 + 1, E10 - 1]) → G10
  50. If(Mod[E11, 3] ≟ 1, E11 + 2, If[Mod[E11, 3] ≟ 2, E11 + 1, E11 - 1]) → G11
  51. If(Mod[E12, 3] ≟ 1, E12 + 2, If[Mod[E12, 3] ≟ 2, E12 + 1, E12 - 1]) → G12
  52. If(C1 ≟ Cell[4, E1] ∨ C1 ≟ Cell[4, F1] ∨ C1 ≟ Cell[4, G1], 1, 0) → H1
  53. If(C2 ≟ Cell[4, E2] ∨ C2 ≟ Cell[4, F2] ∨ C2 ≟ Cell[4, G2], 1, 0) → H2
  54. If(C3 ≟ Cell[4, E3] ∨ C3 ≟ Cell[4, F3] ∨ C3 ≟ Cell[4, G3], 1, 0) → H3
  55. If(C4 ≟ Cell[4, E4] ∨ C4 ≟ Cell[4, F4] ∨ C4 ≟ Cell[4, G4], 1, 0) → H4
  56. If(C5 ≟ Cell[4, E5] ∨ C5 ≟ Cell[4, F5] ∨ C5 ≟ Cell[4, G5], 1, 0) → H5
  57. If(C6 ≟ Cell[4, E6] ∨ C6 ≟ Cell[4, F6] ∨ C6 ≟ Cell[4, G6], 1, 0) → H6
  58. If(C7 ≟ Cell[4, E7] ∨ C7 ≟ Cell[4, F7] ∨ C7 ≟ Cell[4, G7], 1, 0) → H7
  59. If(C8 ≟ Cell[4, E8] ∨ C8 ≟ Cell[4, F8] ∨ C8 ≟ Cell[4, G8], 1, 0) → H8
  60. If(C9 ≟ Cell[4, E9] ∨ C9 ≟ Cell[4, F9] ∨ C9 ≟ Cell[4, G9], 1, 0) → H9
  61. If(C10 ≟ Cell[4, E10] ∨ C10 ≟ Cell[4, F10] ∨ C10 ≟ Cell[4, G10], 1, 0) → H10
  62. If(C11 ≟ Cell[4, E11] ∨ C11 ≟ Cell[4, F11] ∨ C11 ≟ Cell[4, G11], 1, 0) → H11
  63. If(C12 ≟ Cell[4, E12] ∨ C12 ≟ Cell[4, F12] ∨ C12 ≟ Cell[4, G12], 1, 0) → H12
  64. Polygon(D_1, E_1, F_1, G_1) → Polígon13, d_3, e_3, f_3, g_3
  65. Segment(G_1, D_1) → k_2
  66. Segment(D_1, E_1) → l_2
  67. Segment(E_1, F_1) → m_2
  68. Segment(F_1, G_1) → n_2
  69. Segment(H_1, M_1) → p_2
  70. Segment(L_1, Q_1) → q_2
  71. Segment(N_1, I_1) → r_2
  72. Segment(P_1, K_1) → s_2
  73. Segment(J_1, O_1) → t_2
  74. Sum(H1:H12) → H13
  75. Random(1, 10) → u
  76. Polygon(S_1, Z_1, W_1, T_1) → Polígon15, s_3, z_1, w_1, t_3
  77. If(L1 ≟ Cell[13, E1], 1, 0) → N1
  78. If(L2 ≟ Cell[13, E2], 1, 0) → N2
  79. If(L3 ≟ Cell[13, E3], 1, 0) → N3
  80. If(L4 ≟ Cell[13, E4], 1, 0) → N4
  81. If(L5 ≟ Cell[13, E5], 1, 0) → N5
  82. If(L6 ≟ Cell[13, E6], 1, 0) → N6
  83. If(L7 ≟ Cell[13, E7], 1, 0) → N7
  84. If(L8 ≟ Cell[13, E8], 1, 0) → N8
  85. If(L9 ≟ Cell[13, E9], 1, 0) → N9
  86. If(L10 ≟ Cell[13, E10], 1, 0) → N10
  87. If(L11 ≟ Cell[13, E11], 1, 0) → N11
  88. If(L12 ≟ Cell[13, E12], 1, 0) → N12
  89. Sum(N1:N12) → N13
  90. If(R1 ≟ Cell[13, E1], 1, 0) → S1
  91. If(R2 ≟ Cell[13, E2], 1, 0) → S2
  92. If(R3 ≟ Cell[13, E3], 1, 0) → S3
  93. If(R4 ≟ Cell[13, E4], 1, 0) → S4
  94. If(R5 ≟ Cell[13, E5], 1, 0) → S5
  95. If(R6 ≟ Cell[13, E6], 1, 0) → S6
  96. If(R7 ≟ Cell[13, E7], 1, 0) → S7
  97. If(R8 ≟ Cell[13, E8], 1, 0) → S8
  98. If(R9 ≟ Cell[13, E9], 1, 0) → S9
  99. If(R10 ≟ Cell[13, E10], 1, 0) → S10
  100. If(R11 ≟ Cell[13, E11], 1, 0) → S11
  101. If(R12 ≟ Cell[13, E12], 1, 0) → S12
  102. Sum(S1:S12) → S13

AI Drawing Prompt Reference

Draw four parallelograms, each with four points. Then randomly select 12 numbers and generate a series of new numbers by adding or subtracting 1 or 2. Finally, use these new numbers as coordinates to draw four more parallelograms.
The prompt above was compiled from the original drawing commands and is for reference only.