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Rick's Fraction Activity with Video

Rick's Fraction Activity with Video
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2020-05-14 23:27
CircleTrigonometryGeometric ConstructionSlider Animation
This example demonstrates the investigation and comparison of fractions through the manipulation of rectangular and circular area models. It involves core math concepts like fractions, area models, geometric distribution, and trigonometry. Constructed using GeoGebra commands and objects such as Point, Circle, OrthogonalLine, Intersect, Rotate, CircleSector, Segment, Vector, Translate, Polygon, Line. Suitable for middle school and above mathematics education for fraction understanding and geometric intuition.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Circle(A, 3) → e
  3. Point(xAxis) → B
  4. OrthogonalLine(A, xAxis) → f
  5. Intersect(e, f, 2) → C
  6. Rotate(C, (360 * ° / b), A) → C'
  7. Rotate(C', (360 * ° / b), A) → C''
  8. Rotate(C'', (360 * ° / b), A) → C'''
  9. Rotate(C''', (360 * ° / b), A) → D
  10. Rotate(D, (360 * ° / b), A) → D'
  11. Rotate(D', (360 * ° / b), A) → D''
  12. Rotate(D'', (360 * ° / b), A) → D'''
  13. Rotate(D''', (360 * ° / b), A) → E
  14. Rotate(E, (360 * ° / b), A) → E'
  15. Rotate(E', (360 * ° / b), A) → E''
  16. Rotate(E'', (360 * ° / b), A) → E'''
  17. Rotate(E''', (360 * ° / b), A) → F
  18. Rotate(F, (360 * ° / b), A) → F'
  19. Rotate(F', (360 * ° / b), A) → F''
  20. Rotate(F'', (360 * ° / b), A) → F'''
  21. Rotate(F''', (360 * ° / b), A) → G
  22. Rotate(G, (360 * ° / b), A) → G'
  23. Rotate(G', (360 * ° / b), A) → G''
  24. Rotate(G'', (360 * ° / b), A) → G'''
  25. CircleSector(A, C, C') → g
  26. CircleSector(A, C', C'') → h
  27. CircleSector(A, C'', C''') → k
  28. CircleSector(A, C''', D) → p
  29. CircleSector(A, D, D') → q
  30. CircleSector(A, D', D'') → r
  31. CircleSector(A, D'', D''') → s
  32. CircleSector(A, D''', E) → t
  33. CircleSector(A, E, E') → c_1
  34. CircleSector(A, E', E'') → d_1
  35. CircleSector(A, E'', E''') → e_1
  36. CircleSector(A, E''', F) → f_1
  37. CircleSector(A, F, F') → g_1
  38. CircleSector(A, F', F'') → h_1
  39. CircleSector(A, F'', F''') → k_1
  40. CircleSector(A, F''', G) → p_1
  41. CircleSector(A, G, G') → q_1
  42. CircleSector(A, G', G'') → r_1
  43. CircleSector(A, G'', G''') → s_1
  44. CircleSector(A, G''', C) → t_1
  45. Segment(A, C) → i
  46. Segment(A, C') → j
  47. Segment(A, C'') → l
  48. Segment(A, C''') → m
  49. Segment(A, D) → n
  50. Segment(A, D') → a_1
  51. Segment(A, D'') → b_1
  52. Segment(A, D''') → i_1
  53. Segment(A, E) → j_1
  54. Segment(A, E') → l_1
  55. Segment(A, E'') → m_1
  56. Segment(A, E''') → n_1
  57. Segment(A, F) → a_2
  58. Segment(A, F') → b_2
  59. Segment(A, F'') → c_2
  60. Segment(A, F''') → d_2
  61. Segment(A, G) → e_2
  62. Segment(A, G') → f_2
  63. Segment(A, G'') → g_2
  64. Segment(A, G''') → h_2
  65. Intersect(e, xAxis, 1) → H
  66. Intersect(e, xAxis, 2) → I
  67. OrthogonalLine(H, xAxis) → i_2
  68. OrthogonalLine(I, xAxis) → j_2
  69. OrthogonalLine(J, i_2) → k_2
  70. OrthogonalLine(K, i_2) → l_2
  71. Intersect(j_2, k_2) → L
  72. Intersect(j_2, l_2) → M
  73. Segment(J, L) → m_2
  74. Segment(K, M) → n_2
  75. Segment(K, J) → p_2
  76. Segment(M, L) → q_2
  77. Vector(J, L) → u
  78. Translate(i_2, Vector[u / b]) → r_2
  79. Translate(i_2, Vector[(u * 2 / b)]) → s_2
  80. Translate(i_2, Vector[(u * 18 / b)]) → t_2
  81. Translate(i_2, Vector[(u * 19 / b)]) → a_3
  82. Translate(i_2, Vector[(u * 17 / b)]) → b_3
  83. Translate(i_2, Vector[(u * 16 / b)]) → c_3
  84. Translate(i_2, Vector[(u * 15 / b)]) → d_3
  85. Translate(i_2, Vector[(u * 14 / b)]) → e_3
  86. Translate(i_2, Vector[(u * 13 / b)]) → f_3
  87. Translate(i_2, Vector[(u * 12 / b)]) → h_3
  88. Translate(i_2, Vector[(u * 11 / b)]) → i_3
  89. Translate(i_2, Vector[(u * 10 / b)]) → j_3
  90. Translate(i_2, Vector[(u * 9 / b)]) → k_3
  91. Translate(i_2, Vector[(u * 8 / b)]) → l_3
  92. Translate(i_2, Vector[(u * 7 / b)]) → m_3
  93. Translate(i_2, Vector[(u * 6 / b)]) → n_3
  94. Translate(i_2, Vector[(u * 5 / b)]) → p_3
  95. Translate(i_2, Vector[(u * 4 / b)]) → q_3
  96. Translate(i_2, Vector[(u * 3 / b)]) → r_3
  97. Intersect(r_2, n_2) → N
  98. Intersect(r_2, m_2) → O
  99. Intersect(s_2, m_2) → P
  100. Intersect(r_3, m_2) → Q
  101. Intersect(q_3, m_2) → R
  102. Intersect(p_3, m_2) → S
  103. Intersect(n_3, m_2) → T
  104. Intersect(m_3, m_2) → U
  105. Intersect(l_3, m_2) → V
  106. Intersect(k_3, m_2) → W
  107. Intersect(j_3, m_2) → Z
  108. Intersect(i_3, m_2) → A_1
  109. Intersect(h_3, m_2) → B_1
  110. Intersect(m_2, f_3) → D_1
  111. Intersect(e_3, m_2) → E_1
  112. Intersect(d_3, m_2) → F_1
  113. Intersect(c_3, m_2) → G_1
  114. Intersect(b_3, m_2) → H_1
  115. Intersect(t_2, m_2) → I_1
  116. Intersect(a_3, m_2) → J_1
  117. Intersect(a_3, n_2) → K_1
  118. Intersect(t_2, n_2) → L_1
  119. Intersect(b_3, n_2) → M_1
  120. Intersect(c_3, n_2) → N_1
  121. Intersect(d_3, n_2) → O_1
  122. Intersect(e_3, n_2) → P_1
  123. Intersect(n_2, h_3) → R_1
  124. Intersect(i_3, n_2) → S_1
  125. Intersect(j_3, n_2) → T_1
  126. Intersect(k_3, n_2) → U_1
  127. Intersect(l_3, n_2) → V_1
  128. Intersect(m_3, n_2) → W_1
  129. Intersect(n_3, n_2) → Z_1
  130. Intersect(p_3, n_2) → A_2
  131. Intersect(q_3, n_2) → B_2
  132. Intersect(r_3, n_2) → C_2
  133. Intersect(s_2, n_2) → D_2
  134. Intersect(f_3, n_2) → C_1
  135. Polygon(J, O, N, K) → poly1, j_4, o, n_4, k_4
  136. Polygon(N, D_2, P, O) → poly2, n_5, d_4, p_4, o_1
  137. Polygon(D_2, C_2, Q, P) → poly3, d_5, c_4, q_4, p_5
  138. Polygon(C_2, B_2, R, Q) → poly4, c_5, b_4, r_4, q_5
  139. Polygon(A_2, B_2, R, S) → poly5, a_4, b_5, r_5, s_3
  140. Polygon(A_2, Z_1, T, S) → poly6, a_5, z_1, t_3, s_4
  141. Polygon(Z_1, W_1, U, T) → poly7, z_2, w_1, u_1, t_4
  142. Polygon(W_1, V_1, V, U) → poly8, w_2, v_1, v, u_2
  143. Polygon(V_1, U_1, W, V) → poly9, v_2, u_3, w, v_3
  144. Polygon(U_1, T_1, Z, W) → poly10, u_4, t_5, z, w_3
  145. Polygon(T_1, S_1, A_1, Z) → poly11, t_6, s_5, a_6, z_3
  146. Polygon(S_1, R_1, B_1, A_1) → poly12, s_6, r_6, b_6, a_7
  147. Polygon(R_1, C_1, D_1, B_1) → poly13, r_7, c_6, d_6, b_7
  148. Polygon(C_1, P_1, E_1, D_1) → poly14, c_7, p_6, e_4, d_7
  149. Polygon(P_1, O_1, F_1, E_1) → poly15, p_7, o_2, f_4, e_5
  150. Polygon(O_1, N_1, G_1, F_1) → poly16, o_3, n_6, g_3, f_5
  151. Polygon(M_1, N_1, G_1, H_1) → poly17, m_4, n_7, g_4, h_4
  152. Polygon(M_1, L_1, I_1, H_1) → poly18, m_5, l_4, i_4, h_5
  153. Polygon(L_1, K_1, J_1, I_1) → poly19, l_5, k_5, j_5, i_5
  154. Polygon(K_1, M, L, J_1) → poly20, k_6, m_6, l_6, j_6
  155. Circle(B, 3) → g_5
  156. Intersect(g_5, xAxis) → Q_1, E_2
  157. OrthogonalLine(Q_1, xAxis) → e_6
  158. OrthogonalLine(B, xAxis) → f_6
  159. Line(E_2, f_6) → g_6
  160. Intersect(k_2, g_6) → H_2
  161. Intersect(l_2, g_6) → I_2
  162. Intersect(g_5, f_6, 1) → J_2
  163. Rotate(J_2, (360 * ° / d), B) → K_2
  164. Rotate(K_2, (360 * ° / d), B) → L_2
  165. Rotate(L_2, (360 * ° / d), B) → M_2
  166. Rotate(M_2, (360 * ° / d), B) → N_2
  167. Rotate(N_2, (360 * ° / d), B) → O_2
  168. Rotate(O_2, (360 * ° / d), B) → P_2
  169. Rotate(P_2, (360 * ° / d), B) → Q_2
  170. Rotate(Q_2, (360 * ° / d), B) → R_2
  171. Rotate(R_2, (360 * ° / d), B) → S_2
  172. Rotate(S_2, (360 * ° / d), B) → T_2
  173. Rotate(T_2, (360 * ° / d), B) → U_2
  174. Rotate(U_2, (360 * ° / d), B) → V_2
  175. Rotate(V_2, (360 * ° / d), B) → W_2
  176. Rotate(W_2, (360 * ° / d), B) → Z_2
  177. Rotate(Z_2, (360 * ° / d), B) → A_3
  178. Rotate(A_3, (360 * ° / d), B) → B_3
  179. Rotate(B_3, (360 * ° / d), B) → C_3
  180. Rotate(C_3, (360 * ° / d), B) → D_3
  181. Rotate(D_3, (360 * ° / d), B) → E_3
  182. CircleSector(B, J_2, K_2) → h_6
  183. CircleSector(B, K_2, L_2) → q_6
  184. CircleSector(B, L_2, M_2) → e_7
  185. CircleSector(B, M_2, N_2) → f_7
  186. CircleSector(B, N_2, O_2) → g_7
  187. CircleSector(B, O_2, P_2) → h_7
  188. CircleSector(B, P_2, Q_2) → k_7
  189. CircleSector(B, Q_2, R_2) → q_7
  190. CircleSector(B, R_2, S_2) → s_7
  191. CircleSector(B, S_2, T_2) → t_7
  192. CircleSector(B, T_2, U_2) → c_8
  193. CircleSector(B, U_2, V_2) → d_8
  194. CircleSector(B, V_2, W_2) → e_8
  195. CircleSector(B, W_2, Z_2) → f_8
  196. CircleSector(B, Z_2, A_3) → g_8
  197. CircleSector(B, A_3, B_3) → h_8
  198. CircleSector(B, B_3, C_3) → k_8
  199. CircleSector(B, C_3, D_3) → p_8
  200. CircleSector(B, D_3, E_3) → q_8
  201. CircleSector(B, E_3, J_2) → r_8
  202. Segment(J_2, B) → i_6
  203. Segment(K_2, B) → i_7
  204. Segment(L_2, B) → j_7
  205. Segment(M_2, B) → l_7
  206. Segment(N_2, B) → m_7
  207. Segment(O_2, B) → a_8
  208. Segment(P_2, B) → b_8
  209. Segment(Q_2, B) → i_8
  210. Segment(R_2, B) → j_8
  211. Segment(S_2, B) → l_8
  212. Segment(T_2, B) → m_8
  213. Segment(U_2, B) → n_8
  214. Segment(V_2, B) → s_8
  215. Segment(W_2, B) → t_8
  216. Segment(Z_2, B) → a_9
  217. Segment(A_3, B) → b_9
  218. Segment(B_3, B) → c_9
  219. Segment(C_3, B) → d_9
  220. Segment(D_3, B) → e_9
  221. Segment(E_3, B) → f_9
  222. Segment(F_2, H_2) → g_9
  223. Segment(G_2, I_2) → h_9
  224. Segment(I_2, H_2) → i_9
  225. Segment(G_2, F_2) → j_9
  226. Vector(F_2, H_2) → v_4
  227. Translate(e_6, Vector[(v_4 * 1 / d)]) → k_9
  228. Translate(e_6, Vector[(v_4 * 2 / d)]) → l_9
  229. Translate(e_6, Vector[(v_4 * 3 / d)]) → m_9
  230. Translate(e_6, Vector[(v_4 * 4 / d)]) → n_9
  231. Translate(e_6, Vector[(v_4 * 5 / d)]) → p_9
  232. Translate(e_6, Vector[(v_4 * 6 / d)]) → q_9
  233. Translate(e_6, Vector[(v_4 * 7 / d)]) → r_9
  234. Translate(e_6, Vector[(v_4 * 8 / d)]) → s_9
  235. Translate(e_6, Vector[(v_4 * 9 / d)]) → t_9
  236. Translate(e_6, Vector[(v_4 * 10 / d)]) → a_{10}
  237. Translate(e_6, Vector[(v_4 * 11 / d)]) → b_{10}
  238. Translate(e_6, Vector[(v_4 * 12 / d)]) → c_{10}
  239. Translate(e_6, Vector[(v_4 * 13 / d)]) → d_{10}
  240. Translate(e_6, Vector[(v_4 * 14 / d)]) → e_{10}
  241. Translate(e_6, Vector[(v_4 * 15 / d)]) → f_{10}
  242. Translate(e_6, Vector[(v_4 * 16 / d)]) → g_{10}
  243. Translate(e_6, Vector[(v_4 * 17 / d)]) → h_{10}
  244. Translate(e_6, Vector[(v_4 * 18 / d)]) → i_{10}
  245. Translate(e_6, Vector[(v_4 * 19 / d)]) → j_{10}
  246. Intersect(g_9, k_9) → F_3
  247. Intersect(k_9, h_9) → G_3
  248. Intersect(l_9, h_9) → H_3
  249. Intersect(m_9, h_9) → I_3
  250. Intersect(n_9, h_9) → J_3
  251. Intersect(p_9, h_9) → K_3
  252. Intersect(q_9, h_9) → L_3
  253. Intersect(r_9, h_9) → M_3
  254. Intersect(s_9, h_9) → N_3
  255. Intersect(t_9, h_9) → O_3
  256. Intersect(a_{10}, h_9) → P_3
  257. Intersect(b_{10}, h_9) → Q_3
  258. Intersect(c_{10}, h_9) → R_3
  259. Intersect(d_{10}, h_9) → S_3
  260. Intersect(e_{10}, h_9) → T_3
  261. Intersect(f_{10}, h_9) → U_3
  262. Intersect(g_{10}, h_9) → V_3
  263. Intersect(h_{10}, h_9) → W_3
  264. Intersect(i_{10}, h_9) → Z_3
  265. Intersect(j_{10}, h_9) → A_4
  266. Intersect(j_{10}, g_9) → B_4
  267. Intersect(i_{10}, g_9) → C_4
  268. Intersect(h_{10}, g_9) → D_4
  269. Intersect(g_{10}, g_9) → E_4
  270. Intersect(f_{10}, g_9) → F_4
  271. Intersect(e_{10}, g_9) → G_4
  272. Intersect(d_{10}, g_9) → H_4
  273. Intersect(c_{10}, g_9) → I_4
  274. Intersect(b_{10}, g_9) → J_4
  275. Intersect(a_{10}, g_9) → K_4
  276. Intersect(t_9, g_9) → L_4
  277. Intersect(s_9, g_9) → M_4
  278. Intersect(r_9, g_9) → N_4
  279. Intersect(q_9, g_9) → O_4
  280. Intersect(p_9, g_9) → P_4
  281. Intersect(n_9, g_9) → Q_4
  282. Intersect(m_9, g_9) → R_4
  283. Intersect(l_9, g_9) → S_4
  284. Polygon(G_2, G_3, F_3, F_2) → poly21, g_{11}, g_{12}, f_{11}, f_{12}
  285. Polygon(G_3, H_3, S_4, F_3) → poly22, g_{13}, h_{11}, s_{10}, f_{13}
  286. Polygon(H_3, I_3, R_4, S_4) → poly23, h_{12}, i_{11}, r_{10}, s_{11}
  287. Polygon(I_3, J_3, Q_4, R_4) → poly24, i_{12}, j_{11}, q_{10}, r_{11}
  288. Polygon(J_3, K_3, P_4, Q_4) → poly25, j_{12}, k_{10}, p_{10}, q_{11}
  289. Polygon(K_3, L_3, O_4, P_4) → poly26, k_{11}, l_{10}, o_4, p_{11}
  290. Polygon(L_3, M_3, N_4, O_4) → poly27, l_{11}, m_{10}, n_{10}, o_5
  291. Polygon(M_3, N_3, M_4, N_4) → poly28, m_{11}, n_{11}, m_{12}, n_{12}
  292. Polygon(N_3, O_3, L_4, M_4) → poly29, n_{13}, o_6, l_{12}, m_{13}
  293. Polygon(O_3, P_3, K_4, L_4) → poly30, o_7, p_{12}, k_{12}, l_{13}
  294. Polygon(P_3, Q_3, J_4, K_4) → poly31, p_{13}, q_{12}, j_{13}, k_{13}
  295. Polygon(Q_3, R_3, I_4, J_4) → poly32, q_{13}, r_{12}, i_{13}, j_{14}
  296. Polygon(R_3, S_3, H_4, I_4) → poly33, r_{13}, s_{12}, h_{13}, i_{14}
  297. Polygon(S_3, T_3, G_4, H_4) → poly34, s_{13}, t_{10}, g_{14}, h_{14}
  298. Polygon(T_3, U_3, F_4, G_4) → poly35, t_{11}, u_5, f_{14}, g_{15}
  299. Polygon(U_3, V_3, E_4, F_4) → poly36, u_6, v_5, e_{11}, f_{15}
  300. Polygon(V_3, W_3, D_4, E_4) → poly37, v_6, w_4, d_{11}, e_{12}
  301. Polygon(W_3, Z_3, C_4, D_4) → poly38, w_5, z_4, c_{11}, d_{12}
  302. Polygon(Z_3, A_4, B_4, C_4) → poly39, z_5, a_{11}, b_{11}, c_{12}
  303. Polygon(A_4, I_2, H_2, B_4) → poly40, a_{12}, i_{15}, h_{15}, b_{12}