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等效分数拼图：拖动方块探索分数等价

等效分数拼图：拖动方块探索分数等价
几何画板及绘图内容加载中，请稍等……
2012-09-03 06:21
多边形几何作图滑块动画轨迹
所属专题 Primary School Mathematics Collection
本示例通过交互式几何拼图演示等效分数的概念。学生通过拖动每个方块上的“Drag”点，观察如何利用圆、点、线段、垂线、交点、对称和中点等 GeoGebra 命令构建分数关系，探索不同图形表示下的分数相等性。核心数学概念包括分数的基本性质、比例关系以及图形化验证等，适合中小学数学课堂及数学奥林匹克培训使用。

GeoGebra 命令及参数

  1. Circle(A, 2) → c
  2. Point(c) → B
  3. Segment(A, B) → a
  4. OrthogonalLine(A, a) → b
  5. Intersect(c, b) → C, D
  6. Mirror(B, b) → B'
  7. Segment(B', D) → d
  8. Segment(D, B) → e
  9. Segment(B, C) → f
  10. Segment(B', C) → g
  11. Midpoint(f) → E
  12. Midpoint(e) → F
  13. Midpoint(d) → G
  14. Midpoint(g) → H
  15. Circle(A_1, 2) → c_1
  16. Point(c_1) → B_1
  17. Segment(A_1, B_1) → a_1
  18. OrthogonalLine(A_1, a_1) → b_1
  19. Intersect(c_1, b_1) → C_1, D_1
  20. Mirror(B_1, b_1) → B'_1
  21. Segment(B'_1, D_1) → d_1
  22. Segment(D_1, B_1) → e_1
  23. Segment(B_1, C_1) → f_1
  24. Segment(B'_1, C_1) → g_1
  25. Midpoint(f_1) → E_1
  26. Midpoint(e_1) → F_1
  27. Midpoint(d_1) → G_1
  28. Midpoint(g_1) → H_1
  29. Circle(A_4, 2) → c_4
  30. Point(c_4) → B_7
  31. Segment(A_4, B_7) → a_4
  32. OrthogonalLine(A_4, a_4) → b_4
  33. Intersect(c_4, b_4) → C_7, D_7
  34. Mirror(B_7, b_4) → B'_7
  35. Segment(B'_7, D_7) → d_4
  36. Segment(D_7, B_7) → e_4
  37. Segment(B_7, C_7) → f_4
  38. Segment(B'_7, C_7) → g_4
  39. Midpoint(f_4) → E_4
  40. Midpoint(e_4) → F_4
  41. Circle(A_5, 2) → c_5
  42. Point(c_5) → B_6
  43. Segment(A_5, B_6) → a_5
  44. OrthogonalLine(A_5, a_5) → b_5
  45. Intersect(c_5, b_5) → C_6, D_6
  46. Mirror(B_6, b_5) → B'_6
  47. Segment(B'_6, D_6) → d_5
  48. Segment(D_6, B_6) → e_5
  49. Segment(B_6, C_6) → f_5
  50. Segment(B'_6, C_6) → g_5
  51. Midpoint(f_5) → E_5
  52. Midpoint(e_5) → F_5
  53. Midpoint(d_5) → G_5
  54. Midpoint(g_5) → H_5
  55. Circle(A_6, 2) → c_6
  56. Point(c_6) → B_5
  57. Segment(A_6, B_5) → a_6
  58. OrthogonalLine(A_6, a_6) → b_6
  59. Intersect(c_6, b_6) → C_5, D_5
  60. Mirror(B_5, b_6) → B'_5
  61. Segment(B'_5, D_5) → d_6
  62. Segment(D_5, B_5) → e_6
  63. Segment(B_5, C_5) → f_6
  64. Segment(B'_5, C_5) → g_6
  65. Midpoint(f_6) → E_6
  66. Midpoint(e_6) → F_6
  67. Midpoint(d_6) → G_6
  68. Midpoint(g_6) → H_6
  69. Circle(A_7, 2) → c_7
  70. Point(c_7) → B_4
  71. Segment(A_7, B_4) → a_7
  72. OrthogonalLine(A_7, a_7) → b_7
  73. Intersect(c_7, b_7) → C_4, D_4
  74. Mirror(B_4, b_7) → B'_4
  75. Segment(B'_4, D_4) → d_7
  76. Segment(D_4, B_4) → e_7
  77. Segment(B_4, C_4) → f_7
  78. Segment(B'_4, C_4) → g_7
  79. Midpoint(e_7) → F_7
  80. Midpoint(d_7) → G_7
  81. Midpoint(g_7) → H_7
  82. Circle(A_8, 2) → c_8
  83. Point(c_8) → B_{15}
  84. Segment(A_8, B_{15}) → a_8
  85. OrthogonalLine(A_8, a_8) → b_8
  86. Intersect(c_8, b_8) → C_{15}, D_{15}
  87. Mirror(B_{15}, b_8) → B'_{15}
  88. Segment(B'_{15}, D_{15}) → d_8
  89. Segment(D_{15}, B_{15}) → e_8
  90. Segment(B_{15}, C_{15}) → f_8
  91. Segment(B'_{15}, C_{15}) → g_8
  92. Midpoint(f_8) → E_8
  93. Midpoint(e_8) → F_8
  94. Midpoint(d_8) → G_8
  95. Midpoint(g_8) → H_8
  96. Circle(A_9, 2) → c_9
  97. Point(c_9) → B_{14}
  98. Segment(A_9, B_{14}) → a_9
  99. OrthogonalLine(A_9, a_9) → b_9
  100. Intersect(c_9, b_9) → C_{14}, D_{14}
  101. Mirror(B_{14}, b_9) → B'_{14}
  102. Segment(B'_{14}, D_{14}) → d_9
  103. Segment(D_{14}, B_{14}) → e_9
  104. Segment(B_{14}, C_{14}) → f_9
  105. Segment(B'_{14}, C_{14}) → g_9
  106. Midpoint(f_9) → E_9
  107. Midpoint(e_9) → F_9
  108. Midpoint(d_9) → G_9
  109. Midpoint(g_9) → H_9
  110. Circle(A_{12}, 2) → c_{12}
  111. Point(c_{12}) → B_{11}
  112. Segment(A_{12}, B_{11}) → a_{12}
  113. OrthogonalLine(A_{12}, a_{12}) → b_{12}
  114. Intersect(c_{12}, b_{12}) → C_{11}, D_{11}
  115. Mirror(B_{11}, b_{12}) → B'_{11}
  116. Segment(B'_{11}, D_{11}) → d_{12}
  117. Segment(D_{11}, B_{11}) → e_{12}
  118. Segment(B_{11}, C_{11}) → f_{12}
  119. Segment(B'_{11}, C_{11}) → g_{12}
  120. Midpoint(f_{12}) → E_{12}
  121. Midpoint(e_{12}) → F_{12}
  122. Midpoint(d_{12}) → G_{12}
  123. Midpoint(g_{12}) → H_{12}
  124. Circle(A_{13}, 2) → c_{13}
  125. Point(c_{13}) → B_{10}
  126. Segment(A_{13}, B_{10}) → a_{13}
  127. OrthogonalLine(A_{13}, a_{13}) → b_{13}
  128. Intersect(c_{13}, b_{13}) → C_{10}, D_{10}
  129. Mirror(B_{10}, b_{13}) → B'_{10}
  130. Segment(B'_{10}, D_{10}) → d_{13}
  131. Segment(D_{10}, B_{10}) → e_{13}
  132. Segment(B_{10}, C_{10}) → f_{13}
  133. Segment(B'_{10}, C_{10}) → g_{13}
  134. Midpoint(f_{13}) → E_{13}
  135. Midpoint(e_{13}) → F_{13}
  136. Midpoint(d_{13}) → G_{13}
  137. Midpoint(g_{13}) → H_{13}
  138. Circle(A_{14}, 2) → c_{14}
  139. Point(c_{14}) → B_9
  140. Segment(A_{14}, B_9) → a_{14}
  141. OrthogonalLine(A_{14}, a_{14}) → b_{14}
  142. Intersect(c_{14}, b_{14}) → C_9, D_9
  143. Mirror(B_9, b_{14}) → B'_9
  144. Segment(B'_9, D_9) → d_{14}
  145. Segment(D_9, B_9) → e_{14}
  146. Segment(B_9, C_9) → f_{14}
  147. Segment(B'_9, C_9) → g_{14}
  148. Midpoint(e_{14}) → F_{14}
  149. Midpoint(d_{14}) → G_{14}
  150. Circle(A_{15}, 2) → c_{15}
  151. Point(c_{15}) → B_8
  152. Segment(A_{15}, B_8) → a_{15}
  153. OrthogonalLine(A_{15}, a_{15}) → b_{15}
  154. Intersect(c_{15}, b_{15}) → C_8, D_8
  155. Mirror(B_8, b_{15}) → B'_8
  156. Segment(B'_8, D_8) → d_{15}
  157. Segment(D_8, B_8) → e_{15}
  158. Segment(B_8, C_8) → f_{15}
  159. Segment(B'_8, C_8) → g_{15}
  160. Midpoint(f_{15}) → E_{15}
  161. Midpoint(e_{15}) → F_{15}
  162. Midpoint(d_{15}) → G_{15}
  163. Midpoint(g_{15}) → H_{15}
  164. Circle(A_{16}, 2) → c_{16}
  165. Point(c_{16}) → B_{19}
  166. Segment(A_{16}, B_{19}) → a_{16}
  167. OrthogonalLine(A_{16}, a_{16}) → b_{16}
  168. Intersect(c_{16}, b_{16}) → C_{19}, D_{19}
  169. Mirror(B_{19}, b_{16}) → B'_{19}
  170. Segment(B'_{19}, D_{19}) → d_{16}
  171. Segment(D_{19}, B_{19}) → e_{16}
  172. Segment(B_{19}, C_{19}) → f_{16}
  173. Segment(B'_{19}, C_{19}) → g_{16}
  174. Midpoint(f_{16}) → E_{16}
  175. Midpoint(e_{16}) → F_{16}
  176. Midpoint(d_{16}) → G_{16}
  177. Midpoint(g_{16}) → H_{16}
  178. Circle(A_{17}, 2) → c_{17}
  179. Point(c_{17}) → B_{18}
  180. Segment(A_{17}, B_{18}) → a_{17}
  181. OrthogonalLine(A_{17}, a_{17}) → b_{17}
  182. Intersect(c_{17}, b_{17}) → C_{18}, D_{18}
  183. Mirror(B_{18}, b_{17}) → B'_{18}
  184. Segment(B'_{18}, D_{18}) → d_{17}
  185. Segment(D_{18}, B_{18}) → e_{17}
  186. Segment(B_{18}, C_{18}) → f_{17}
  187. Segment(B'_{18}, C_{18}) → g_{17}
  188. Midpoint(d_{17}) → G_{17}
  189. Midpoint(g_{17}) → H_{17}
  190. Circle(A_{18}, 2) → c_{18}
  191. Point(c_{18}) → B_{17}
  192. Segment(A_{18}, B_{17}) → a_{18}
  193. OrthogonalLine(A_{18}, a_{18}) → b_{18}
  194. Intersect(c_{18}, b_{18}) → C_{17}, D_{17}
  195. Mirror(B_{17}, b_{18}) → B'_{17}
  196. Segment(B'_{17}, D_{17}) → d_{18}
  197. Segment(D_{17}, B_{17}) → e_{18}
  198. Segment(B_{17}, C_{17}) → f_{18}
  199. Segment(B'_{17}, C_{17}) → g_{18}
  200. Midpoint(f_{18}) → E_{18}
  201. Midpoint(g_{18}) → H_{18}
  202. Circle(A_{19}, 2) → c_{19}
  203. Point(c_{19}) → B_{16}
  204. Segment(A_{19}, B_{16}) → a_{19}
  205. OrthogonalLine(A_{19}, a_{19}) → b_{19}
  206. Intersect(c_{19}, b_{19}) → C_{16}, D_{16}
  207. Mirror(B_{16}, b_{19}) → B'_{16}
  208. Segment(B'_{16}, D_{16}) → d_{19}
  209. Segment(D_{16}, B_{16}) → e_{19}
  210. Segment(B_{16}, C_{16}) → f_{19}
  211. Segment(B'_{16}, C_{16}) → g_{19}
  212. Midpoint(f_{19}) → E_{19}
  213. Midpoint(e_{19}) → F_{19}
  214. Midpoint(d_{19}) → G_{19}
  215. Midpoint(g_{19}) → H_{19}
  216. Midpoint(f_7) → I
  217. Segment(J, K) → h
  218. OrthogonalLine(J, h) → i
  219. OrthogonalLine(K, h) → j
  220. Point(i) → L
  221. OrthogonalLine(L, i) → k
  222. Intersect(j, k) → M
  223. Segment(J, L) → l
  224. Segment(L, M) → m
  225. Segment(M, K) → n
  226. Segment(K, J) → p

AI 绘图提示语参考

画一个几何拼图，通过拖动点探索分数等价。在两个正方形中，分别画圆、点、线段和垂直线，找到交点，镜像点，连接点形成新的线段。计算线段的中点，并画出新的圆和线段。展示如何通过几何构造和图形验证分数等价关系，适合小学生和初中生学习分数的基本性质、比例关系和图形验证。
以上提示语为根据原始绘图命令整理而来，仅供参考。