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Equivalent Fractions by Melissa (2)

Equivalent Fractions by Melissa (2)
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2020-01-29 02:29
TransformationGeometric Construction
This example dynamically demonstrates the equivalence of fractions through geometric transformations, illustrating the geometric meaning of fractions. Core math concepts include fractions, geometric transformations, similar figures, LCM, and GCD. Construction involves commands like Segment, Point, Polygon, and objects such as f, K, L, M for transformations and annotations, with sliders to visualize fraction changes. Suitable for middle school and above mathematics education to understand the connection between fractions and geometric transformations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Point(f) → C
  3. Point(f) → G
  4. Segment(B, K) → g
  5. Point(Circle[D_5, 2]) → E_5
  6. Polygon(D_5, E_5, F_5, G_5) → q1, d_5, e_5, f_5, g_5
  7. Point(Circle[P_5, 2]) → Q_5
  8. Polygon(P_5, Q_5, R_5, S_5) → q2, p_5, q_5, r_5, s_5
  9. Point(Circle[Z_5, 2]) → A_6
  10. Polygon(Z_5, A_6, B_6, C_6) → q3, z_5, a_6, b_6, c_6
  11. Point(Circle[D_6, 2]) → E_6
  12. Polygon(D_6, E_6, F_6, G_6) → q4, d_6, e_6, f_6, g_6
  13. Point(Circle[P_6, 3.7076237040084377]) → Q_6
  14. Point(Circle[Z_6, 6.692047753852707]) → A_7
  15. Polygon(Z_6, A_7, B_7, C_7) → q5, z_6, a_7, b_7, c_7
  16. Point(Circle[Z_7, 6.692047753852707]) → A_8
  17. Polygon(Z_7, A_8, B_8, C_8) → q5_1, z_1, a_1, b_1, c_1
  18. Point(Circle[Z_8, 6.692047753852707]) → A_9
  19. Polygon(Z_8, A_9, B_9, C_9) → q5_2, z_2, a_2, b_2, c_2
  20. Point(Circle[P_7, 2]) → Q_7
  21. Polygon(P_7, Q_7, R_7, S_7) → q2_1, p_1, q_1, r_1, s_1
  22. Point(Circle[P_8, 2]) → Q_8
  23. Polygon(P_8, Q_8, R_8, S_8) → q2_2, p_2, q_2, r_2, s_2
  24. Point(Circle[P_9, 2]) → Q_9
  25. Polygon(P_9, Q_9, R_9, S_9) → q2_3, p_3, q_3, r_3, s_3
  26. Point(Circle[D_7, 2]) → E_7
  27. Polygon(D_7, E_7, F_7, G_7) → q1_1, d_1, e_1, f_1, g_1
  28. Point(Circle[Z_9, 2]) → A_{10}
  29. Polygon(Z_9, A_{10}, B_{10}, C_{10}) → q3_1, z_3, a_3, b_3, c_3
  30. Point(Circle[Z_{10}, 2]) → A_{11}
  31. Polygon(Z_{10}, A_{11}, B_{11}, C_{11}) → q3_2, z_4, a_4, b_4, c_4
  32. Point(Circle[Z_{11}, 2]) → A_{12}
  33. Polygon(Z_{11}, A_{12}, B_{12}, C_{12}) → q3_3, z_7, a_5, b_5, c_5
  34. Point(Circle[Z_{12}, 2]) → A_{13}
  35. Polygon(Z_{12}, A_{13}, B_{13}, C_{13}) → q3_4, z_8, a_8, b_8, c_8
  36. Point(Circle[Z_{13}, 2]) → A_{14}
  37. Polygon(Z_{13}, A_{14}, B_{14}, C_{14}) → q3_5, z_9, a_9, b_9, c_9
  38. Point(Circle[Z_{14}, 2]) → A_{15}
  39. Polygon(Z_{14}, A_{15}, B_{15}, C_{15}) → q3_6, z_{10}, a_{10}, b_{10}, c_{10}
  40. Point(Circle[Z_{15}, 2]) → A_{16}
  41. Polygon(Z_{15}, A_{16}, B_{16}, C_{16}) → q3_7, z_{11}, a_{11}, b_{11}, c_{11}
  42. Point(Circle[D_8, 2]) → E_8
  43. Polygon(D_8, E_8, F_8, G_8) → q4_1, d_2, e_2, f_2, g_2
  44. Point(Circle[D_9, 2]) → E_9
  45. Polygon(D_9, E_9, F_9, G_9) → q4_2, d_3, e_3, f_3, g_3
  46. Point(Circle[D_{10}, 2]) → E_{10}
  47. Polygon(D_{10}, E_{10}, F_{10}, G_{10}) → q4_3, d_4, e_4, f_4, g_4
  48. Point(Circle[D_{11}, 2]) → E_{11}
  49. Polygon(D_{11}, E_{11}, F_{11}, G_{11}) → q4_4, d_7, e_7, f_7, g_7
  50. Point(Circle[D_{12}, 2]) → E_{12}
  51. Polygon(D_{12}, E_{12}, F_{12}, G_{12}) → q4_5, d_8, e_8, f_8, g_8
  52. Point(Circle[D_{13}, 2]) → E_{13}
  53. Polygon(D_{13}, E_{13}, F_{13}, G_{13}) → q4_6, d_9, e_9, f_9, g_9
  54. Point(Circle[D_{14}, 2]) → E_{14}
  55. Polygon(D_{14}, E_{14}, F_{14}, G_{14}) → q4_7, d_{10}, e_{10}, f_{10}, g_{10}
  56. Point(Circle[D_{15}, 2]) → E_{15}
  57. Polygon(D_{15}, E_{15}, F_{15}, G_{15}) → q4_8, d_{11}, e_{11}, f_{11}, g_{11}
  58. Point(Circle[D_{16}, 2]) → E_{16}
  59. Polygon(D_{16}, E_{16}, F_{16}, G_{16}) → q4_9, d_{12}, e_{12}, f_{12}, g_{12}
  60. Point(Circle[I_7, 3.318493038763244]) → J_7
  61. Polygon(I_7, J_7, K_7, I_8) → q6, i_7, j_7, k_7, i_8
  62. Point(Circle[I_9, 3.318493038763244]) → J_8
  63. Polygon(I_9, J_8, K_8, I_{10}) → q6_1, i_1, j_1, k_1, i_2
  64. Point(Circle[I_{11}, 3.318493038763244]) → J_9
  65. Polygon(I_{11}, J_9, K_9, I_{12}) → q6_2, i_3, j_2, k_2, i_4
  66. Point(Circle[I_{13}, 3.318493038763244]) → J_{10}
  67. Polygon(I_{13}, J_{10}, K_{10}, I_{14}) → q6_3, i_5, j_3, k_3, i_6
  68. Point(Circle[I_{15}, 3.318493038763244]) → J_{11}
  69. Polygon(I_{15}, J_{11}, K_{11}, I_{16}) → q6_4, i_9, j_4, k_4, i_{10}
  70. Point(Circle[I_{17}, 3.318493038763244]) → J_{12}
  71. Polygon(I_{17}, J_{12}, K_{12}, I_{18}) → q6_5, i_{11}, j_5, k_5, i_{12}
  72. Point(Circle[P_{10}, 4]) → Q_{10}
  73. Polygon(P_{10}, Q_{10}, R_{10}, S_{10}) → q7, p_{10}, q_{10}, r_{10}, s_{10}
  74. Point(Circle[P_{11}, 4]) → Q_{11}
  75. Polygon(P_{11}, Q_{11}, R_{11}, S_{11}) → q7_1, p_4, q_4, r_4, s_4
  76. Point(Circle[P_{12}, 4]) → Q_{12}
  77. Polygon(P_{12}, Q_{12}, R_{12}, S_{12}) → q7_2, p_6, q_6, r_6, s_6
  78. Point(Circle[P_{13}, 4]) → Q_{13}
  79. Polygon(P_{13}, Q_{13}, R_{13}, S_{13}) → q7_3, p_7, q_7, r_7, s_7
  80. Point(Circle[P_{14}, 4]) → Q_{14}
  81. Polygon(P_{14}, Q_{14}, R_{14}, S_{14}) → q7_4, p_8, q_8, r_8, s_8
  82. Point(Circle[J_{14}, 2.8477655083416864]) → K_{14}
  83. Polygon(J_{14}, K_{14}, H_{15}, J_{15}) → q8, j_{14}, k_{14}, h_{15}, j_{15}
  84. Point(Circle[J_{13}, 2.8477655083416864]) → K_{13}
  85. Polygon(J_{13}, K_{13}, H_{13}, J_{16}) → q8_1, j_6, k_6, h_1, j_8
  86. Point(Circle[J_{17}, 2.8477655083416864]) → K_{15}
  87. Polygon(J_{17}, K_{15}, H_{14}, J_{18}) → q8_2, j_9, k_8, h_2, j_{10}
  88. Point(Circle[J_{19}, 2.8477655083416864]) → K_{16}
  89. Polygon(J_{19}, K_{16}, H_{16}, J_{20}) → q8_3, j_{11}, k_9, h_3, j_{12}
  90. Point(Circle[J_{21}, 2.8477655083416864]) → K_{17}
  91. Polygon(J_{21}, K_{17}, H_{17}, J_{22}) → q8_4, j_{16}, k_{10}, h_4, j_{13}
  92. Point(Circle[J_{23}, 2.8477655083416864]) → K_{18}
  93. Polygon(J_{23}, K_{18}, H_{18}, J_{24}) → q8_5, j_{17}, k_{11}, h_5, j_{18}
  94. Point(Circle[J_{25}, 2.8477655083416864]) → K_{19}
  95. Polygon(J_{25}, K_{19}, H_{19}, J_{26}) → q8_6, j_{19}, k_{12}, h_6, j_{20}
  96. Point(Circle[P_{15}, 2.2024410791962357]) → Q_{15}
  97. Polygon(P_{15}, Q_{15}, R_{15}, S_{15}) → q9, p_{15}, q_{15}, r_{15}, s_{15}
  98. Point(Circle[P_{16}, 2.2024410791962357]) → Q_{16}
  99. Polygon(P_{16}, Q_{16}, R_{16}, S_{16}) → q9_1, p_9, q_9, r_9, s_9
  100. Point(Circle[P_{17}, 2.2024410791962357]) → Q_{17}
  101. Polygon(P_{17}, Q_{17}, R_{17}, S_{17}) → q9_2, p_{11}, q_{11}, r_{11}, s_{11}
  102. Point(Circle[P_{18}, 2.2024410791962357]) → Q_{18}
  103. Polygon(P_{18}, Q_{18}, R_{18}, S_{18}) → q9_3, p_{12}, q_{12}, r_{12}, s_{12}
  104. Point(Circle[P_{19}, 2.2024410791962357]) → Q_{19}
  105. Polygon(P_{19}, Q_{19}, R_{19}, S_{19}) → q9_4, p_{13}, q_{13}, r_{13}, s_{13}
  106. Point(Circle[P_{20}, 2.2024410791962357]) → Q_{20}
  107. Polygon(P_{20}, Q_{20}, R_{20}, S_{20}) → q9_5, p_{14}, q_{14}, r_{14}, s_{14}
  108. Point(Circle[P_{21}, 2.2024410791962357]) → Q_{21}
  109. Polygon(P_{21}, Q_{21}, R_{21}, S_{21}) → q9_6, p_{16}, q_{16}, r_{16}, s_{16}
  110. Point(Circle[P_{22}, 2.2024410791962357]) → Q_{22}
  111. Polygon(P_{22}, Q_{22}, R_{22}, S_{22}) → q9_7, p_{17}, q_{17}, r_{17}, s_{17}
  112. Point(Circle[P_{23}, 2.2024410791962357]) → Q_{23}
  113. Polygon(P_{23}, Q_{23}, R_{23}, S_{23}) → q9_8, p_{18}, q_{18}, r_{18}, s_{18}
  114. Point(Circle[Z_{16}, 20]) → A_{17}
  115. Polygon(Z_{16}, A_{17}, B_{17}, C_{17}) → q10, z_{16}, a_{17}, b_{17}, c_{17}

AI Drawing Prompt Reference

Draw a horizontal segment with two movable points dividing it into three parts. Construct a series of squares of varying sizes along the segment, with side lengths controlled by sliders. Use geometric transformations (translation, scaling) to demonstrate equivalent fractions: divide the whole shape into equal parts, shade some regions, and ensure that different fractions correspond to equal area proportions. Include multiple groups of similar squares, each representing a fraction, and adjust sliders to change the number of divisions, visually comparing fraction values.
The prompt above was compiled from the original drawing commands and is for reference only.