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Equivalent Fractions Puzzle: Drag and Explore Fraction Equivalence

Equivalent Fractions Puzzle: Drag and Explore Fraction Equivalence
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2012-09-03 06:21
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In collections Primary School Mathematics Collection
This example demonstrates the concept of equivalent fractions through an interactive geometric puzzle. Users can drag the "Drag" point on each square to explore how circles, points, segments, orthogonal lines, intersections, mirrors, and midpoints are used in GeoGebra to construct and visualize fraction equivalence. The core mathematical ideas include the fundamental properties of fractions, proportional relationships, and graphical verification, making it suitable for elementary and middle school mathematics classes as well as math contest preparation.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a geometric puzzle to explore fraction equivalence by dragging points. In two squares, draw circles, points, segments, and perpendicular lines, find intersections, mirror points, and connect them to form new segments. Calculate midpoints of segments, draw new circles and segments. Show how geometric construction and graphical verification can demonstrate fraction equivalence, suitable for elementary and middle school students learning fundamental properties of fractions, proportional relationships, and graphical proof.
The prompt above was compiled from the original drawing commands and is for reference only.