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Equivalent Fractions Circle Area Model

Equivalent Fractions Circle Area Model
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2015-03-03 02:59
CircleGeometric ConstructionSlider Animation
This example demonstrates equivalent fractions using circle area models. Key mathematical concepts include fraction equivalence, area proportion, and the relationship with π. Construction involves GeoGebra commands like Circle, CircleSector, and Segment to build area models, with Intersect used to verify equivalence. Suitable for elementary high school or middle school math classes to visually understand the connection between fractions and geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 3) → c_6
  3. Point(xAxis) → C
  4. Circle(C, 1.5) → d
  5. OrthogonalLine(C, xAxis) → a_1
  6. Intersect(d, a_1, 2) → D
  7. Intersect(d, a_1, 1) → E
  8. OrthogonalLine(D, a_1) → e
  9. OrthogonalLine(E, a_1) → f
  10. Point(xAxis) → F
  11. OrthogonalLine(F, e) → g_2
  12. Intersect(e, g_2) → G
  13. Point(g_2) → H
  14. Intersect(c_6, yAxis, 1) → B
  15. Rotate(B, (360 * ° / b), A) → B'
  16. CircleSector(A, B, B') → k
  17. Rotate(B', (360 * ° / b), A) → B''
  18. Rotate(B'', (360 * ° / b), A) → B'''
  19. Rotate(B''', (360 * ° / b), A) → I
  20. Rotate(I, (360 * ° / b), A) → I'
  21. Rotate(I', (360 * ° / b), A) → I''
  22. Rotate(I'', (360 * ° / b), A) → I'''
  23. Rotate(I''', (360 * ° / b), A) → J
  24. Rotate(J, (360 * ° / b), A) → J'
  25. CircleSector(A, B', B'') → p
  26. CircleSector(A, B'', B''') → q
  27. CircleSector(A, B''', I) → r
  28. CircleSector(A, I, I') → s_6
  29. CircleSector(A, I', I'') → t
  30. CircleSector(A, I'', I''') → c_1
  31. CircleSector(A, I''', J) → f_1
  32. CircleSector(A, J, J') → k_1
  33. CircleSector(A, J', B) → p_1
  34. Segment(B, A) → i
  35. Segment(B', A) → j
  36. Segment(B'', A) → l
  37. Segment(B''', A) → m
  38. Segment(I, A) → n
  39. Segment(I', A) → b_1
  40. Segment(I'', A) → i_1
  41. Segment(I''', A) → j_1
  42. Segment(J, A) → l_1
  43. Segment(J', A) → m_1
  44. Circle(A, B) → q_1
  45. Rotate(B, (360 * ° / ((b * s))), A) → B'_1
  46. Rotate(B'_1, (360 * ° / ((b * s))), A) → K
  47. Rotate(K, (360 * ° / ((b * s))), A) → K'
  48. Rotate(K', (360 * ° / ((b * s))), A) → K''
  49. Rotate(B', (360 * ° / ((b * s))), A) → B''_1
  50. Rotate(B''_1, (360 * ° / ((b * s))), A) → L
  51. Rotate(L, (360 * ° / ((b * s))), A) → L'
  52. Rotate(L', (360 * ° / ((b * s))), A) → L''
  53. Rotate(B'', (360 * ° / ((b * s))), A) → B'''_1
  54. Rotate(B'''_1, (360 * ° / ((b * s))), A) → M
  55. Rotate(M, (360 * ° / ((b * s))), A) → M'
  56. Rotate(M', (360 * ° / ((b * s))), A) → M''
  57. Rotate(B''', (360 * ° / ((b * s))), A) → N
  58. Rotate(N, (360 * ° / ((b * s))), A) → N'
  59. Rotate(N', (360 * ° / ((b * s))), A) → N''
  60. Rotate(N'', (360 * ° / ((b * s))), A) → N'''
  61. Rotate(I, (360 * ° / ((b * s))), A) → I'_1
  62. Rotate(I'_1, (360 * ° / ((b * s))), A) → O
  63. Rotate(O, (360 * ° / ((b * s))), A) → O'
  64. Rotate(O', (360 * ° / ((b * s))), A) → O''
  65. Rotate(I', (360 * ° / ((b * s))), A) → I''_1
  66. Rotate(I''_1, (360 * ° / ((b * s))), A) → P
  67. Rotate(P, (360 * ° / ((b * s))), A) → P'
  68. Rotate(P', (360 * ° / ((b * s))), A) → P''
  69. Rotate(I'', (360 * ° / ((b * s))), A) → I'''_1
  70. Rotate(I'''_1, (360 * ° / ((b * s))), A) → Q
  71. Rotate(Q, (360 * ° / ((b * s))), A) → Q'
  72. Rotate(Q', (360 * ° / ((b * s))), A) → Q''
  73. Rotate(I''', (360 * ° / ((b * s))), A) → R
  74. Rotate(R, (360 * ° / ((b * s))), A) → R'
  75. Rotate(R', (360 * ° / ((b * s))), A) → R''
  76. Rotate(R'', (360 * ° / ((b * s))), A) → R'''
  77. Rotate(J, (360 * ° / ((b * s))), A) → J'_1
  78. Rotate(J'_1, (360 * ° / ((b * s))), A) → S
  79. Rotate(S, (360 * ° / ((b * s))), A) → S'
  80. Rotate(S', (360 * ° / ((b * s))), A) → S''
  81. Rotate(J', (360 * ° / ((b * s))), A) → J''
  82. Rotate(J'', (360 * ° / ((b * s))), A) → J'''
  83. Rotate(J''', (360 * ° / ((b * s))), A) → T
  84. Rotate(T, (360 * ° / ((b * s))), A) → T'
  85. Vector(B'_1, A) → u
  86. Translate(B'_1, Vector[(u * c)]) → U
  87. Circle(A, U) → r_1
  88. Segment(K, A) → n_1
  89. Segment(K', A) → s_1
  90. Segment(K'', A) → t_1
  91. Segment(B''_1, A) → a_2
  92. Segment(L, A) → b_2
  93. Segment(L', A) → c_2
  94. Segment(L'', A) → d_2
  95. Segment(B'''_1, A) → e_2
  96. Segment(M, A) → f_2
  97. Segment(M', A) → h_2
  98. Segment(M'', A) → i_2
  99. Segment(N, A) → j_2
  100. Segment(N', A) → k_2
  101. Segment(N'', A) → l_2
  102. Segment(N''', A) → m_2
  103. Segment(I'_1, A) → n_2
  104. Segment(O, A) → p_2
  105. Segment(O', A) → q_2
  106. Segment(O'', A) → r_2
  107. Segment(I''_1, A) → s_2
  108. Segment(P, A) → t_2
  109. Segment(P', A) → a_3
  110. Segment(P'', A) → b_3
  111. Segment(I'''_1, A) → c_3
  112. Segment(Q, A) → d_3
  113. Segment(Q', A) → e_3
  114. Segment(Q'', A) → f_3
  115. Segment(R, A) → g_3
  116. Segment(R', A) → h_3
  117. Segment(R'', A) → i_3
  118. Segment(R''', A) → j_3
  119. Segment(J'_1, A) → k_3
  120. Segment(S, A) → l_3
  121. Segment(S', A) → m_3
  122. Segment(S'', A) → n_3
  123. Segment(J'', A) → p_3
  124. Segment(J''', A) → q_3
  125. Segment(T, A) → r_3
  126. Segment(T', A) → s_3
  127. Intersect(r_1, n_1) → V,
  128. Intersect(r_1, s_1) → W,
  129. Intersect(r_1, t_1) → Z,
  130. Intersect(r_1, a_2) → A_1,
  131. Intersect(b_2, c_2) → B_1
  132. Intersect(r_1, b_2) → C_1,
  133. Intersect(r_1, c_2) → D_1,
  134. Intersect(r_1, d_2) → E_1,
  135. Intersect(r_1, e_2, 1) → F_1
  136. Intersect(r_1, f_2, 1) → G_1
  137. Intersect(r_1, h_2, 1) → H_1
  138. Intersect(r_1, i_2, 1) → I_1
  139. Intersect(r_1, j_2, 1) → J_1
  140. Intersect(r_1, k_2, 1) → K_1
  141. Intersect(r_1, l_2, 1) → L_1
  142. Intersect(r_1, m_2, 1) → M_1
  143. Intersect(r_1, n_2, 1) → N_1
  144. Intersect(r_1, p_2, 1) → O_1
  145. Intersect(r_1, q_2, 1) → P_1
  146. Intersect(r_1, r_2, 1) → Q_1
  147. Intersect(r_1, s_2, 1) → R_1
  148. Intersect(r_1, t_2, 1) → S_1
  149. Intersect(r_1, a_3, 1) → T_1
  150. Intersect(r_1, b_3, 1) → U_1
  151. Intersect(r_1, c_3, 1) → V_1
  152. Intersect(r_1, d_3, 1) → W_1
  153. Intersect(r_1, e_3, 1) → Z_1
  154. Intersect(r_1, f_3, 1) → A_2
  155. Intersect(r_1, g_3, 1) → B_2
  156. Intersect(r_1, h_3, 1) → C_2
  157. Intersect(r_1, i_3, 1) → D_2
  158. Intersect(r_1, j_3, 1) → E_2
  159. Intersect(r_1, k_3, 1) → F_2
  160. Intersect(r_1, l_3, 1) → G_2
  161. Intersect(r_1, m_3, 1) → H_2
  162. Intersect(r_1, n_3, 1) → I_2
  163. Intersect(r_1, p_3, 1) → J_2
  164. Intersect(r_1, q_3, 1) → K_2
  165. Intersect(r_1, r_3, 1) → L_2
  166. Intersect(r_1, s_3, 1) → M_2
  167. Segment(B'_1, U) → t_3
  168. Segment(K, V) → a_4
  169. Segment(K', W) → b_4
  170. Segment(K'', Z) → c_4
  171. Segment(B''_1, A_1) → d_4
  172. Segment(L, C_1) → e_4
  173. Segment(L', D_1) → f_4
  174. Segment(L'', E_1) → g_4
  175. Segment(B'''_1, F_1) → h_4
  176. Segment(M, G_1) → i_4
  177. Segment(M', H_1) → j_4
  178. Segment(M'', I_1) → k_4
  179. Segment(N, J_1) → l_4
  180. Segment(N', K_1) → m_4
  181. Segment(N'', L_1) → n_4
  182. Segment(N''', M_1) → p_4
  183. Segment(I'_1, N_1) → q_4
  184. Segment(O, O_1) → r_4
  185. Segment(O', P_1) → s_4
  186. Segment(O'', Q_1) → t_4
  187. Segment(I''_1, R_1) → a_5
  188. Segment(P, S_1) → b_5
  189. Segment(P', T_1) → c_5
  190. Segment(P'', U_1) → d_5
  191. Segment(I'''_1, V_1) → e_5
  192. Segment(Q, W_1) → f_5
  193. Segment(Q', Z_1) → g_5
  194. Segment(Q'', A_2) → h_5
  195. Segment(R, B_2) → i_5
  196. Segment(R', C_2) → j_5
  197. Segment(R'', D_2) → k_5
  198. Segment(R''', E_2) → l_5
  199. Segment(J'_1, F_2) → m_5
  200. Segment(S, G_2) → n_5
  201. Segment(S', H_2) → p_5
  202. Segment(S'', I_2) → q_5
  203. Segment(J'', J_2) → r_5
  204. Segment(J''', K_2) → s_5
  205. Segment(T, L_2) → t_5
  206. Segment(T', M_2) → a_6
  207. Circle(A, B) → h
  208. Segment(B, A) → d_1
  209. Intersect(r_1, d_1, 1) → N_2
  210. Segment(B, N_2) → e_1

AI Drawing Prompt Reference

Draw a circle with a radius of 3, then draw multiple sectors on this circle to represent equivalent fractions. Start by drawing a circle with a radius of 1.5, then use rotation and intersection operations to generate multiple sectors, each with an angle that is a multiple of 360 divided by b, where b is a slider-controlled value.
The prompt above was compiled from the original drawing commands and is for reference only.