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Exploring Equivalent Fractions

Exploring Equivalent Fractions
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2020-06-23 23:14
TransformationGeometric Construction
This example demonstrates how to find equivalent fractions using geometric transformations. Key mathematical concepts include the equivalence of fractions. Using GeoGebra commands such as Segment, OrthogonalLine, Point, Circle, Intersect, Dilate, and Polygon, an equivalent fraction model is constructed. Suitable for high-grade elementary or junior high school students to learn the basic concepts and equivalence of fractions.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. OrthogonalLine(B, a) → c
  4. Point(b) → C
  5. Circle(A, C) → d
  6. Intersect(d, b) → D, E
  7. Circle(C, A) → e
  8. Circle(E, A) → f
  9. Intersect(e, b, 2) → F
  10. Intersect(f, b, 2) → G
  11. OrthogonalLine(F, b) → g
  12. OrthogonalLine(C, b) → h
  13. OrthogonalLine(E, b) → i
  14. OrthogonalLine(G, b) → j
  15. Intersect(c, h) → H
  16. Intersect(c, g) → I
  17. Intersect(c, i) → J
  18. Intersect(c, j) → K
  19. Segment(F, I) → k
  20. Segment(I, H) → l
  21. Segment(H, C) → m
  22. Segment(C, F) → n
  23. Segment(E, J) → p
  24. Segment(J, K) → q
  25. Segment(K, G) → r
  26. Segment(G, E) → s
  27. Dilate(H, 1 / top, C) → H'
  28. Dilate(H, 2 / top, C) → H'_1
  29. Dilate(H, 3 / top, C) → H'_2
  30. Dilate(H, 4 / top, C) → H'_3
  31. Dilate(H, 5 / top, C) → H'_4
  32. Dilate(H, 6 / top, C) → H'_5
  33. Dilate(H, 7 / top, C) → H'_6
  34. Dilate(H, 8 / top, C) → H'_7
  35. Dilate(H, 9 / top, C) → H'_8
  36. Dilate(H, 10 / top, C) → H'_9
  37. Dilate(H, 11 / top, C) → H'_{10}
  38. OrthogonalLine(H', m) → t
  39. OrthogonalLine(H'_1, m) → a_1
  40. OrthogonalLine(H'_2, m) → b_1
  41. OrthogonalLine(H'_3, m) → c_1
  42. OrthogonalLine(H'_4, m) → d_1
  43. OrthogonalLine(H'_5, m) → e_1
  44. OrthogonalLine(H'_6, m) → f_1
  45. OrthogonalLine(H'_7, m) → g_1
  46. OrthogonalLine(H'_8, m) → h_1
  47. OrthogonalLine(H'_9, m) → i_1
  48. OrthogonalLine(H'_{10}, m) → j_1
  49. Intersect(t, k) → L
  50. Intersect(a_1, k) → M
  51. Intersect(b_1, k) → N
  52. Intersect(c_1, k) → O
  53. Intersect(d_1, k) → P
  54. Intersect(e_1, k) → Q
  55. Intersect(f_1, k) → R
  56. Intersect(g_1, k) → S
  57. Intersect(h_1, k) → T
  58. Intersect(i_1, k) → U
  59. Intersect(j_1, k) → V
  60. Polygon(C, F, L, H') → poly1, c_2, f_2, l_1, h'
  61. Polygon(L, M, H'_1, H') → poly2, l_2, m_1, h'_1, h'_2
  62. Polygon(M, N, H'_2, H'_1) → poly3, m_2, n_1, h'_3, h'_4
  63. Polygon(N, O, H'_3, H'_2) → poly4, n_2, o, h'_5, h'_6
  64. Polygon(O, P, H'_4, H'_3) → poly5, o_1, p_1, h'_7, h'_8
  65. Polygon(P, Q, H'_5, H'_4) → poly6, p_2, q_1, h'_9, h'_{10}
  66. Polygon(Q, R, H'_6, H'_5) → poly7, q_2, r_1, h'_{11}, h'_{12}
  67. Polygon(R, S, H'_7, H'_6) → poly8, r_2, s_1, h'_{13}, h'_{14}
  68. Polygon(S, T, H'_8, H'_7) → poly9, s_2, t_1, h'_{15}, h'_{16}
  69. Polygon(T, U, H'_9, H'_8) → poly10, t_2, u, h'_{17}, h'_{18}
  70. Polygon(U, V, H'_{10}, H'_9) → poly11, u_1, v, h'_{19}, h'_{20}
  71. Polygon(V, I, H, H'_{10}) → poly12, v_1, i_2, h_2, h'_{21}
  72. Dilate(J, 1 / bottom, E) → J'
  73. Dilate(J, 2 / bottom, E) → J'_1
  74. Dilate(J, 3 / bottom, E) → J'_2
  75. Dilate(J, 4 / bottom, E) → J'_3
  76. Dilate(J, 5 / bottom, E) → J'_4
  77. Dilate(J, 6 / bottom, E) → J'_5
  78. Dilate(J, 7 / bottom, E) → J'_6
  79. Dilate(J, 8 / bottom, E) → J'_7
  80. Dilate(J, 9 / bottom, E) → J'_8
  81. Dilate(J, 10 / bottom, E) → J'_9
  82. Dilate(J, 11 / bottom, E) → J'_{10}
  83. OrthogonalLine(J', p) → k_1
  84. OrthogonalLine(J'_1, p) → a_2
  85. OrthogonalLine(J'_2, p) → b_2
  86. OrthogonalLine(J'_3, p) → d_2
  87. OrthogonalLine(J'_4, p) → e_2
  88. OrthogonalLine(J'_5, p) → g_2
  89. OrthogonalLine(J'_6, p) → j_2
  90. OrthogonalLine(J'_7, p) → k_2
  91. OrthogonalLine(J'_8, p) → a_3
  92. OrthogonalLine(J'_9, p) → b_3
  93. OrthogonalLine(J'_{10}, p) → c_3
  94. Intersect(k_1, r) → W
  95. Intersect(a_2, r) → Z
  96. Intersect(b_2, r) → A_1
  97. Intersect(d_2, r) → B_1
  98. Intersect(e_2, r) → C_1
  99. Intersect(g_2, r) → D_1
  100. Intersect(j_2, r) → E_1
  101. Intersect(k_2, r) → F_1
  102. Intersect(a_3, r) → G_1
  103. Intersect(b_3, r) → H_1
  104. Intersect(c_3, r) → I_1
  105. Polygon(E, J', W, G) → poly13, e_3, j', w, g_3
  106. Polygon(J', J'_1, Z, W) → poly14, j'_1, j'_2, z, w_1
  107. Polygon(J'_1, J'_2, A_1, Z) → poly15, j'_3, j'_4, a_4, z_1
  108. Polygon(J'_2, J'_3, B_1, A_1) → poly16, j'_5, j'_6, b_4, a_5
  109. Polygon(J'_3, J'_4, C_1, B_1) → poly17, j'_7, j'_8, c_4, b_5
  110. Polygon(J'_4, J'_5, D_1, C_1) → poly18, j'_9, j'_{10}, d_3, c_5
  111. Polygon(J'_5, J'_6, E_1, D_1) → poly19, j'_{11}, j'_{12}, e_4, d_4
  112. Polygon(J'_6, J'_7, F_1, E_1) → poly20, j'_{13}, j'_{14}, f_3, e_5
  113. Polygon(J'_7, J'_8, G_1, F_1) → poly21, j'_{15}, j'_{16}, g_4, f_4
  114. Polygon(J'_8, J'_9, H_1, G_1) → poly22, j'_{17}, j'_{18}, h_3, g_5
  115. Polygon(J'_9, J'_{10}, I_1, H_1) → poly23, j'_{19}, j'_{20}, i_3, h_4
  116. Polygon(J'_{10}, J, K, I_1) → poly24, j'_{21}, j_3, k_3, i_4

AI Drawing Prompt Reference

Draw a geometric diagram to show how to find equivalent fractions through geometric transformations. Start by drawing a line segment, then draw perpendicular lines at both ends of the segment. Take a point on the segment and draw a circle with this point as the center, intersecting the perpendicular lines at two points. Draw circles with these two points as centers, intersecting the perpendicular lines at four more points. Connect these points to form a quadrilateral, and then demonstrate equivalent fractions by scaling and drawing perpendicular lines from one side of the quadrilateral.
The prompt above was compiled from the original drawing commands and is for reference only.