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分母为200和300的等价分数可视化

分母为200和300的等价分数可视化
几何画板及绘图内容加载中，请稍等……
2015-08-19 17:01
多边形变换几何作图滑块动画
该GeoGebra范例通过动态图形直观展示等价分数的关系，具体演示20/100、40/200、60/300以及30/100、60/200、90/300这三组分数在数值上的相等性。核心数学概念是分数的等价性，即分子分母按相同比例缩放时分数值不变。作图要点包括：使用多边形（Polygon）构造面积模型，通过交点（Intersect）、中点（Midpoint）、线段（Segment）和垂线（OrthogonalLine）等命令划分区域，并利用镜像（Mirror）等变换辅助展示分数对应的部分。该范例适合小学高年级至初中阶段的学生学习分数概念，也可用于教师课堂演示，帮助学生直观理解等价分数的几何意义。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  4. Midpoint(D, C) → E
  5. Midpoint(C, B) → F
  6. Midpoint(A, B) → G
  7. Midpoint(D, A) → H
  8. Point(c) → I
  9. Point(c) → J
  10. Point(c) → K
  11. Point(c) → L
  12. Point(c) → M
  13. Point(c) → N
  14. Point(c) → O
  15. Point(c) → P
  16. Point(d) → Q
  17. Point(d) → R
  18. Point(d) → S
  19. Point(d) → T
  20. Point(d) → U
  21. Point(d) → V
  22. Point(d) → W
  23. Point(d) → Z
  24. Point(b) → A_1
  25. Point(b) → B_1
  26. Point(b) → C_1
  27. Point(b) → D_1
  28. Point(b) → E_1
  29. Point(b) → F_1
  30. Point(b) → G_1
  31. Point(b) → H_1
  32. Point(a) → I_1
  33. Point(a) → J_1
  34. Point(a) → K_1
  35. Point(a) → L_1
  36. Point(a) → M_1
  37. Point(a) → N_1
  38. Point(a) → O_1
  39. Point(a) → P_1
  40. Segment(I, P_1) → e
  41. Segment(J, O_1) → f
  42. Segment(K, N_1) → g
  43. Segment(L, M_1) → h
  44. Segment(E, G) → i
  45. Segment(M, L_1) → j
  46. Segment(N, K_1) → k
  47. Segment(O, J_1) → l
  48. Segment(P, I_1) → m
  49. Segment(Q, A_1) → n
  50. Segment(R, B_1) → p
  51. Segment(S, C_1) → q
  52. Segment(T, D_1) → r
  53. Segment(H, F) → s
  54. Segment(U, E_1) → t
  55. Segment(V, F_1) → a_1
  56. Segment(W, G_1) → b_1
  57. Segment(Z, H_1) → c_1
  58. Point(yAxis) → Q_1
  59. Point(yAxis) → R_1
  60. Segment(Q_1, R_1) → d_1
  61. OrthogonalLine(R_1, d_1) → e_1
  62. Point(e_1) → Move_1
  63. OrthogonalLine(Move_1, e_1) → f_1
  64. Mirror(poly1, f_1) → poly2
  65. Mirror(I, f_1) → I'
  66. Mirror(P_1, f_1) → T_1
  67. Segment(I', T_1) → e'
  68. Mirror(J, f_1) → J'
  69. Mirror(O_1, f_1) → U_1
  70. Segment(J', U_1) → f'
  71. Mirror(K, f_1) → K'
  72. Mirror(N_1, f_1) → V_1
  73. Segment(K', V_1) → g'
  74. Mirror(L, f_1) → L'
  75. Mirror(M_1, f_1) → W_1
  76. Segment(L', W_1) → h'
  77. Mirror(E, f_1) → E'
  78. Mirror(G, f_1) → G'
  79. Segment(E', G') → i'
  80. Mirror(M, f_1) → M'
  81. Mirror(L_1, f_1) → Z_1
  82. Segment(M', Z_1) → j'
  83. Mirror(N, f_1) → N'
  84. Mirror(K_1, f_1) → A_2
  85. Segment(N', A_2) → k'
  86. Mirror(O, f_1) → O'
  87. Mirror(J_1, f_1) → B_2
  88. Segment(O', B_2) → l'
  89. Mirror(P, f_1) → P'
  90. Mirror(I_1, f_1) → C_2
  91. Segment(P', C_2) → m'
  92. Mirror(Q, f_1) → Q'
  93. Mirror(A_1, f_1) → D_2
  94. Segment(Q', D_2) → n'
  95. Mirror(R, f_1) → R'
  96. Mirror(B_1, f_1) → E_2
  97. Segment(R', E_2) → p'
  98. Mirror(S, f_1) → S'
  99. Mirror(C_1, f_1) → F_2
  100. Segment(S', F_2) → q'
  101. Mirror(T, f_1) → T'
  102. Mirror(D_1, f_1) → G_2
  103. Segment(T', G_2) → r'
  104. Mirror(H, f_1) → H'
  105. Mirror(F, f_1) → F'
  106. Segment(H', F') → s'
  107. Mirror(U, f_1) → U'
  108. Mirror(E_1, f_1) → H_2
  109. Segment(U', H_2) → t'
  110. Mirror(V, f_1) → V'
  111. Mirror(F_1, f_1) → I_2
  112. Segment(V', I_2) → g_1
  113. Mirror(W, f_1) → W'
  114. Mirror(G_1, f_1) → J_2
  115. Segment(W', J_2) → h_1
  116. Mirror(Z, f_1) → Z'
  117. Mirror(H_1, f_1) → K_2
  118. Segment(Z', K_2) → i_1
  119. Point(e_1) → Move_2
  120. OrthogonalLine(Move_2, d_1) → j_1
  121. OrthogonalLine(Move_2, e_1) → k_1
  122. Mirror(poly2, k_1) → poly3
  123. Mirror(I', k_1) → I''
  124. Mirror(T_1, k_1) → M_2
  125. Segment(I'', M_2) → e''
  126. Mirror(J', k_1) → J''
  127. Mirror(U_1, k_1) → N_2
  128. Segment(J'', N_2) → f''
  129. Mirror(K', k_1) → K''
  130. Mirror(V_1, k_1) → O_2
  131. Segment(K'', O_2) → g''
  132. Mirror(L', k_1) → L''
  133. Mirror(W_1, k_1) → P_2
  134. Segment(L'', P_2) → h''
  135. Mirror(E', k_1) → E''
  136. Mirror(G', k_1) → G''
  137. Segment(E'', G'') → i''
  138. Mirror(M', k_1) → M''
  139. Mirror(Z_1, k_1) → Q_2
  140. Segment(M'', Q_2) → j''
  141. Mirror(N', k_1) → N''
  142. Mirror(A_2, k_1) → R_2
  143. Segment(N'', R_2) → k''
  144. Mirror(O', k_1) → O''
  145. Mirror(B_2, k_1) → S_2
  146. Segment(O'', S_2) → l''
  147. Mirror(P', k_1) → P''
  148. Mirror(C_2, k_1) → T_2
  149. Segment(P'', T_2) → m''
  150. Mirror(Q', k_1) → Q''
  151. Mirror(D_2, k_1) → U_2
  152. Segment(Q'', U_2) → n''
  153. Mirror(R', k_1) → R''
  154. Mirror(E_2, k_1) → V_2
  155. Segment(R'', V_2) → p''
  156. Mirror(S', k_1) → S''
  157. Mirror(F_2, k_1) → W_2
  158. Segment(S'', W_2) → q''
  159. Mirror(T', k_1) → T''
  160. Mirror(G_2, k_1) → Z_2
  161. Segment(T'', Z_2) → r''
  162. Mirror(H', k_1) → H''
  163. Mirror(F', k_1) → F''
  164. Segment(H'', F'') → s''
  165. Mirror(U', k_1) → U''
  166. Mirror(H_2, k_1) → A_3
  167. Segment(U'', A_3) → t''
  168. Mirror(V', k_1) → V''
  169. Mirror(I_2, k_1) → B_3
  170. Segment(V'', B_3) → l_1
  171. Mirror(W', k_1) → W''
  172. Mirror(J_2, k_1) → C_3
  173. Segment(W'', C_3) → m_1
  174. Mirror(Z', k_1) → Z''
  175. Mirror(K_2, k_1) → D_3
  176. Segment(Z'', D_3) → n_1
  177. Polygon(S_1, E_3, F_3, G_3) → s60, s_1, e_3, f_3, g_3
  178. Mirror(S_1, f_1) → H_3
  179. Mirror(E_3, f_1) → I_3
  180. Mirror(F_3, f_1) → J_3
  181. Mirror(G_3, f_1) → K_3
  182. Polygon(H_3, I_3, J_3, K_3) → s60', h_3, i_3, j_3, k_3
  183. Mirror(H_3, k_1) → L_3
  184. Mirror(I_3, k_1) → M_3
  185. Mirror(J_3, k_1) → N_3
  186. Mirror(K_3, k_1) → O_3
  187. Polygon(L_3, M_3, N_3, O_3) → s60'', l_3, m_3, n_3, o_3
  188. Polygon(P_3, Q_3, R_3, S_3) → poly4, p_3, q_3, r_3, s_3
  189. Mirror(P_3, f_1) → T_3
  190. Mirror(Q_3, f_1) → U_3
  191. Mirror(R_3, f_1) → V_3
  192. Mirror(S_3, f_1) → W_3
  193. Polygon(T_3, U_3, V_3, W_3) → poly4', t_3, u_3, v_3, w_3
  194. Polygon(Z_3, A_4, B_4, C_4) → poly5, z_3, a_4, b_4, c_4
  195. Mirror(Z_3, f_1) → D_4
  196. Mirror(A_4, f_1) → E_4
  197. Mirror(B_4, f_1) → F_4
  198. Mirror(C_4, f_1) → G_4
  199. Polygon(D_4, E_4, F_4, G_4) → poly5', d_4, e_4, f_4, g_4
  200. Polygon(H_4, I_4, J_4, K_4) → poly6, h_4, i_4, j_4, k_4
  201. Mirror(H_4, f_1) → L_4
  202. Mirror(I_4, f_1) → M_4
  203. Mirror(J_4, f_1) → N_4
  204. Mirror(K_4, f_1) → O_4
  205. Polygon(L_4, M_4, N_4, O_4) → poly6', l_4, m_4, n_4, o_4
  206. Mirror(L_4, k_1) → P_4
  207. Mirror(M_4, k_1) → Q_4
  208. Mirror(N_4, k_1) → R_4
  209. Mirror(O_4, k_1) → S_4
  210. Polygon(P_4, Q_4, R_4, S_4) → poly6'', p_4, q_4, r_4, s_4

AI 绘图提示语参考

绘制一个由坐标轴交点出发的正方形，其底边在横轴上。将正方形上下两边各等分为若干段，并在左右两边也做相应划分，用线段连接上下对应的分点，形成网格。再在正方形内部添加水平和垂直的中线，以及连接各边中点的线段，使图形呈现对称的分割。整体展示分数等值的面积模型，通过网格和辅助线直观体现不同分母下相同比例的区域划分。
以上提示语为根据原始绘图命令整理而来，仅供参考。