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Fraction Addition Demonstration by Daniel Mentrard

Fraction Addition Demonstration by Daniel Mentrard
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2020-02-28 15:42
PolygonVectorGeometric Construction
This example visually demonstrates the addition of fractions through geometric transformations, illustrating the process of fraction addition. It involves core mathematical concepts such as fraction operations, geometric transformations, vector and polygon constructions. Key GeoGebra commands and objects used include Mod, Segment, Translate, Rotate, Sequence, Polygon, and Vector to achieve precise geometric constructions and dynamic demonstrations. Suitable for middle school and above mathematics education, aiding in understanding the connection between fraction addition and geometric transformations, and enhancing spatial reasoning skills.

GeoGebra Commands & Parameters

  1. Mod((q * m), p) → qq
  2. Segment(A, B) → a
  3. Segment(A, D) → b
  4. Segment(D, C) → c
  5. Segment(C, B) → d
  6. Translate(E, Vector[A, B]) → F
  7. Rotate(F, 90°, E) → H
  8. Rotate(E, 90°, H) → G
  9. Segment(E, F) → e
  10. Segment(F, G) → f
  11. Segment(G, H) → g
  12. Segment(H, E) → h
  13. Sequence(Segment[A + ((i * w / p), 0), A + ((i * w / p), w)], i, 1, p - 1) → list1
  14. Sequence(Segment[E + ((i * w / p), 0), E + ((i * w / p), w)], i, 1, p - 1) → list2
  15. Sequence(Segment[A + (0, (i * w / m)), A + (w, (i * w / m))], i, 1, m - 1) → list3
  16. Sequence(Segment[E + (0, (i * w / m)), E + (w, (i * w / m))], i, 1, m - 1) → list4
  17. Polygon(E, E + (w, 0), E + (w, (n / m * w)), E + (0, (n / m * w))) → poly1, e_1, i, j, k
  18. Polygon(A, A + ((q / p * w), 0), A + ((q / p * w), w), A + (0, w)) → poly2, a_1, l, r, s_1
  19. Polygon(I, I + (w, 0), I + (w, (n / m * w)), I + (0, (n / m * w))) → poly3, i_1, s, t, b_1
  20. Sequence(Segment[I + (0, (i * w / m)), I + (w, (i * w / m))], i, 1, m - 1) → liste1
  21. Sequence(Segment[M + ((i * w / p), 0), M + ((i * w / p), w)], i, 1, p - 1) → liste2
  22. Polygon(I, J, K, L) → poly4, i_2, j_1, k_1, l_1
  23. Polygon(M, M + ((q / p * w), 0), M + ((q / p * w), w), M + (0, w)) → poly5, m_1, c_1, d_1, f_1
  24. Polygon(M, N, O, P) → poly6, m_2, n_1, o_1, p_1
  25. Vector(E, Q) → u
  26. Translate(G, u) → G'
  27. Translate(H, u) → H'
  28. Segment(G', H') → g'
  29. Translate(list2, u) → list2'
  30. Translate(F, u) → F'
  31. Translate(G, u) → G'_1
  32. Segment(F', G'_1) → f'
  33. Translate(H, u) → H'_1
  34. Translate(E, u) → E'
  35. Segment(H'_1, E') → h'
  36. Translate(E, u) → E'_1
  37. Translate(F, u) → F'_1
  38. Segment(E'_1, F'_1) → e'
  39. Translate(poly1, u) → poly1'
  40. Translate(list4, u) → list4'
  41. Vector(A, T) → v
  42. Translate(C, v) → C'
  43. Translate(B, v) → B'
  44. Segment(C', B') → d'
  45. Translate(list3, v) → list3'
  46. Translate(A, v) → A'
  47. Translate(B, v) → B'_1
  48. Segment(A', B'_1) → a'
  49. Translate(list1, v) → list1'
  50. Translate(D, v) → D'
  51. Translate(C, v) → C'_1
  52. Segment(D', C'_1) → c'
  53. Translate(A, v) → A'_1
  54. Translate(D, v) → D'_1
  55. Segment(A'_1, D'_1) → b'
  56. Polygon(V, W, B', T) → poly8, v_1, w_1, b'_1, t_1
  57. Polygon(Z, B_1, A_1, V) → poly9, z, b_2, a_2, v_2
  58. Vector(T, R) → u_1
  59. Translate(V, u_1) → V'
  60. Translate(W, u_1) → W'
  61. Translate(B', u_1) → B''
  62. Translate(T, u_1) → T'
  63. Polygon(V', W', B'', T') → poly8', v', w', b'', t'
  64. Translate(Z, u_1) → Z'
  65. Translate(B_1, u_1) → S
  66. Translate(A_1, u_1) → C_1
  67. Translate(V, u_1) → V'_1
  68. Polygon(Z', S, C_1, V'_1) → poly9', z', s_2, c_2, v'_1
  69. CircumcircleArc(D_1, E_1, F_1) → g_1
  70. Point(g_1) → G_1
  71. Vector(G_1, F_1) → z_1
  72. Line(H_1, I_1) → h_1
  73. Line(J_1, K_1) → q_1
  74. Segment(W', B'') → r_1
  75. Segment(V', W') → d_2
  76. Segment(W', B'') → f_2
  77. Segment(V'_1, T') → g_2
  78. Segment(V'_1, Z') → h_2
  79. Segment(S, C_1) → j_2
  80. Vector(L_1, M_1) → u_2
  81. Vector(N_1, O_1) → w_2
  82. Sequence(Segment[V'_1 + ((i * w / p), 0), Z' + ((i * w / p), 0)], i, 1, p) → liste42
  83. Sequence(Segment[T' + ((i * w / p), 0), V' + ((i * w / p), 0)], i, 1, p) → liste41
  84. Translate(P_1, u_1) → Q_1
  85. Segment(Z', Q_1) → e_2
  86. Segment(W', G') → k_2
  87. Sequence(Segment[T' + (0, (i * w / m)), T' + (w, (i * w / m))], i, 1, pp) → liste40
  88. Line(R_1, S_1) → l_2