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Investigating Adding Fractions

Investigating Adding Fractions
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2011-10-23 07:19
TransformationGeometric Construction
This example demonstrates the process of adding fractions. Key mathematical concepts include fraction addition. Using GeoGebra commands such as OrthogonalLine, Circle, Intersect, etc., a geometric model of fraction addition is constructed. Suitable for high-grade elementary or junior high school students to learn fraction addition.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A, yAxis) → e
  2. OrthogonalLine(A, e) → f
  3. Circle(A, size) → h
  4. Intersect(h, e, 1.0) → B
  5. Intersect(h, f, 2.0) → C
  6. Intersect(h, e, 1.0) → D
  7. OrthogonalLine(B, e) → i
  8. Intersect(h, f, 2.0) → E
  9. OrthogonalLine(C, f) → j
  10. Intersect(i, j) → F
  11. Polygon(A, B, F, C) → P, a_1, b_1, f_1, c_1
  12. Circle(A, VarRadius) → k
  13. Intersect(k, a_1) → G,
  14. Circle(G, A) → p
  15. Intersect(p, a_1, 2.0) → H
  16. Circle(H, G) → q
  17. Intersect(q, a_1) → I, J
  18. Circle(J, H) → r
  19. Intersect(r, a_1) → K, L
  20. Circle(L, J) → s
  21. Intersect(s, a_1) → M, N
  22. Circle(N, L) → t
  23. Intersect(t, a_1) → O, Q
  24. Circle(Q, N) → d_1
  25. Intersect(d_1, a_1) → R, S
  26. Circle(S, Q) → e_1
  27. Intersect(e_1, a_1) → T, U
  28. Circle(U, S) → g_1
  29. Intersect(g_1, a_1) → V, W
  30. Circle(W, U) → h_1
  31. OrthogonalLine(G, a_1) → l
  32. OrthogonalLine(H, a_1) → m
  33. OrthogonalLine(J, a_1) → n
  34. OrthogonalLine(L, a_1) → i_1
  35. OrthogonalLine(N, a_1) → j_1
  36. OrthogonalLine(Q, a_1) → k_1
  37. OrthogonalLine(S, a_1) → l_1
  38. OrthogonalLine(U, a_1) → m_1
  39. OrthogonalLine(W, a_1) → n_1
  40. Intersect(f_1, l) → Y
  41. Intersect(f_1, m) → Z
  42. Intersect(f_1, n) → A_1
  43. Intersect(f_1, i_1) → B_1
  44. Intersect(f_1, j_1) → C_1
  45. Intersect(f_1, k_1) → D_1
  46. Intersect(l_1, f_1) → E_1
  47. Intersect(f_1, m_1) → F_1
  48. Intersect(f_1, n_1) → G_1
  49. Ray(A, B) → p_1
  50. Point(p_1) → H_1
  51. Vector(A, H_1) → u
  52. Translate(A, u) → A'
  53. Translate(B, u) → B'
  54. Translate(F, u) → F'
  55. Translate(C, u) → C'
  56. Polygon(A', B', F', C') → P', a', b', f', c'
  57. OrthogonalLine(V, a_1) → q_1
  58. Circle(V, U) → r_1
  59. Segment(G, Y) → s_1
  60. Segment(H, Z) → t_1
  61. Segment(J, A_1) → a_2
  62. Segment(L, B_1) → b_2
  63. Segment(N, C_1) → c_2
  64. Segment(Q, D_1) → d_2
  65. Segment(S, E_1) → e_2
  66. Segment(U, F_1) → f_2
  67. Segment(W, G_1) → g_2
  68. Circle(H_1, VarRadius_2) → h_2
  69. Intersect(h_2, c', 1.0) → J_1
  70. Circle(J_1, H_1) → k_2
  71. Intersect(k_2, c', 2.0) → K_1
  72. Circle(K_1, J_1) → p_2
  73. Intersect(p_2, c', 2.0) → L_1
  74. Circle(L_1, K_1) → q_2
  75. Intersect(q_2, c', 2.0) → M_1
  76. Circle(M_1, L_1) → r_2
  77. Intersect(r_2, c', 2.0) → N_1
  78. Circle(N_1, M_1) → s_2
  79. Intersect(s_2, c') → O_1, P_1
  80. Circle(P_1, N_1) → t_2
  81. Intersect(t_2, c', 2.0) → Q_1
  82. Circle(Q_1, P_1) → c_3
  83. Intersect(c_3, c', 2.0) → R_1
  84. Circle(R_1, Q_1) → d_3
  85. Intersect(d_3, c', 2.0) → S_1
  86. Circle(S_1, R_1) → e_3
  87. OrthogonalLine(J_1, c') → i_2
  88. OrthogonalLine(K_1, c') → j_2
  89. OrthogonalLine(L_1, c') → l_2
  90. OrthogonalLine(M_1, c') → m_2
  91. OrthogonalLine(N_1, c') → n_2
  92. OrthogonalLine(P_1, c') → a_3
  93. OrthogonalLine(Q_1, c') → b_3
  94. OrthogonalLine(R_1, c') → f_3
  95. OrthogonalLine(S_1, c') → g_3
  96. Intersect(b', i_2) → T_1
  97. Intersect(b', j_2) → U_1
  98. Intersect(b', l_2) → V_1
  99. Intersect(b', m_2) → W_1
  100. Intersect(b', n_2) → Y_1
  101. Intersect(b', a_3) → Z_1
  102. Intersect(b', b_3) → A_2
  103. Intersect(b', f_3) → B_2
  104. Intersect(b', g_3) → C_2
  105. Segment(J_1, T_1) → h_3
  106. Segment(U_1, K_1) → i_3
  107. Segment(L_1, V_1) → j_3
  108. Segment(W_1, M_1) → k_3
  109. Segment(N_1, Y_1) → l_3
  110. Segment(Z_1, P_1) → m_3
  111. Segment(Q_1, A_2) → n_3
  112. Segment(B_2, R_1) → p_3
  113. Segment(S_1, C_2) → q_3
  114. Circle(A, VarWidth_1) → r_3
  115. Intersect(r_3, a_1) → D_2, S_2
  116. OrthogonalLine(D_2, f_1) → s_3
  117. Intersect(s_3, f_1) → E_2
  118. OrthogonalLine(E_2, s_3) → t_3
  119. Intersect(t_3, c_1) → F_2
  120. Polygon(A, D_2, E_2, F_2) → P_2, a_4, d_4, e_4, f_4
  121. OrthogonalLine(O, a_1) → b_4
  122. Intersect(b_4, f_1) → G_2
  123. Circle(O, N) → g_4
  124. Circle(O_1, N_1) → q_4
  125. OrthogonalLine(O_1, c') → t_4
  126. Circle(H_1, VarWidth_2) → h_5
  127. Intersect(h_5, c') → F_3,
  128. OrthogonalLine(F_3, c') → i_5
  129. Intersect(i_5, b') → G_3
  130. Polygon(H_1, F_3, G_3, B') → P_3, h_6, f_6, g_6, b'_1