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分数识别

分数识别
几何画板及绘图内容加载中，请稍等……
2016-07-18 23:53
概率统计几何作图函数图像
①本范例演示如何通过图形化方式识别分数；②涉及的核心数学概念包括分数、几何图形、概率统计；③作图要点——从下方『构造摘要』提炼用到了 Sequence（数列）、Random（随机数）、IndexOf（索引）、If（条件判断）、Sum（求和）、Polygon（多边形）、Point（点）、Segment（线段）等 GeoGebra 命令/对象；④适合初中及以上学生学习分数、概率统计及几何作图。

GeoGebra 命令及参数

  1. Sequence(Sample[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, 12, false], i, 1, 10) → matriu1
  2. Random(1, 10) → fila
  3. IndexOf(1, Element[matriu1, fila]) → E1
  4. IndexOf(2, Element[matriu1, fila]) → E2
  5. IndexOf(3, Element[matriu1, fila]) → E3
  6. IndexOf(4, Element[matriu1, fila]) → E4
  7. IndexOf(5, Element[matriu1, fila]) → E5
  8. IndexOf(6, Element[matriu1, fila]) → E6
  9. IndexOf(7, Element[matriu1, fila]) → E7
  10. IndexOf(8, Element[matriu1, fila]) → E8
  11. IndexOf(9, Element[matriu1, fila]) → E9
  12. IndexOf(10, Element[matriu1, fila]) → E10
  13. IndexOf(11, Element[matriu1, fila]) → E11
  14. IndexOf(12, Element[matriu1, fila]) → E12
  15. If(Mod[E1, 3] ≟ 1, E1 + 1, If[Mod[E1, 3] ≟ 2, E1 - 1, E1 - 2]) → F1
  16. If(Mod[E2, 3] ≟ 1, E2 + 1, If[Mod[E2, 3] ≟ 2, E2 - 1, E2 - 2]) → F2
  17. If(Mod[E3, 3] ≟ 1, E3 + 1, If[Mod[E3, 3] ≟ 2, E3 - 1, E3 - 2]) → F3
  18. If(Mod[E4, 3] ≟ 1, E4 + 1, If[Mod[E4, 3] ≟ 2, E4 - 1, E4 - 2]) → F4
  19. If(Mod[E5, 3] ≟ 1, E5 + 1, If[Mod[E5, 3] ≟ 2, E5 - 1, E5 - 2]) → F5
  20. If(Mod[E6, 3] ≟ 1, E6 + 1, If[Mod[E6, 3] ≟ 2, E6 - 1, E6 - 2]) → F6
  21. If(Mod[E7, 3] ≟ 1, E7 + 1, If[Mod[E7, 3] ≟ 2, E7 - 1, E7 - 2]) → F7
  22. If(Mod[E8, 3] ≟ 1, E8 + 1, If[Mod[E8, 3] ≟ 2, E8 - 1, E8 - 2]) → F8
  23. If(Mod[E9, 3] ≟ 1, E9 + 1, If[Mod[E9, 3] ≟ 2, E9 - 1, E9 - 2]) → F9
  24. If(Mod[E10, 3] ≟ 1, E10 + 1, If[Mod[E10, 3] ≟ 2, E10 - 1, E10 - 2]) → F10
  25. If(Mod[E11, 3] ≟ 1, E11 + 1, If[Mod[E11, 3] ≟ 2, E11 - 1, E11 - 2]) → F11
  26. If(Mod[E12, 3] ≟ 1, E12 + 1, If[Mod[E12, 3] ≟ 2, E12 - 1, E12 - 2]) → F12
  27. IndexOf(10, Element[matriu1, fila]) → o
  28. If(Mod[E1, 3] ≟ 1, E1 + 2, If[Mod[E1, 3] ≟ 2, E1 + 1, E1 - 1]) → G1
  29. If(Mod[E2, 3] ≟ 1, E2 + 2, If[Mod[E2, 3] ≟ 2, E2 + 1, E2 - 1]) → G2
  30. If(Mod[E3, 3] ≟ 1, E3 + 2, If[Mod[E3, 3] ≟ 2, E3 + 1, E3 - 1]) → G3
  31. If(Mod[E4, 3] ≟ 1, E4 + 2, If[Mod[E4, 3] ≟ 2, E4 + 1, E4 - 1]) → G4
  32. If(Mod[E5, 3] ≟ 1, E5 + 2, If[Mod[E5, 3] ≟ 2, E5 + 1, E5 - 1]) → G5
  33. If(Mod[E6, 3] ≟ 1, E6 + 2, If[Mod[E6, 3] ≟ 2, E6 + 1, E6 - 1]) → G6
  34. If(Mod[E7, 3] ≟ 1, E7 + 2, If[Mod[E7, 3] ≟ 2, E7 + 1, E7 - 1]) → G7
  35. If(Mod[E8, 3] ≟ 1, E8 + 2, If[Mod[E8, 3] ≟ 2, E8 + 1, E8 - 1]) → G8
  36. If(Mod[E9, 3] ≟ 1, E9 + 2, If[Mod[E9, 3] ≟ 2, E9 + 1, E9 - 1]) → G9
  37. If(Mod[E10, 3] ≟ 1, E10 + 2, If[Mod[E10, 3] ≟ 2, E10 + 1, E10 - 1]) → G10
  38. If(Mod[E11, 3] ≟ 1, E11 + 2, If[Mod[E11, 3] ≟ 2, E11 + 1, E11 - 1]) → G11
  39. If(Mod[E12, 3] ≟ 1, E12 + 2, If[Mod[E12, 3] ≟ 2, E12 + 1, E12 - 1]) → G12
  40. If(C1 ≟ Cell[4, E1] ∨ C1 ≟ Cell[4, F1] ∨ C1 ≟ Cell[4, G1], 1, 0) → H1
  41. If(C2 ≟ Cell[4, E2] ∨ C2 ≟ Cell[4, F2] ∨ C2 ≟ Cell[4, G2], 1, 0) → H2
  42. If(C3 ≟ Cell[4, E3] ∨ C3 ≟ Cell[4, F3] ∨ C3 ≟ Cell[4, G3], 1, 0) → H3
  43. If(C4 ≟ Cell[4, E4] ∨ C4 ≟ Cell[4, F4] ∨ C4 ≟ Cell[4, G4], 1, 0) → H4
  44. If(C5 ≟ Cell[4, E5] ∨ C5 ≟ Cell[4, F5] ∨ C5 ≟ Cell[4, G5], 1, 0) → H5
  45. If(C6 ≟ Cell[4, E6] ∨ C6 ≟ Cell[4, F6] ∨ C6 ≟ Cell[4, G6], 1, 0) → H6
  46. If(C7 ≟ Cell[4, E7] ∨ C7 ≟ Cell[4, F7] ∨ C7 ≟ Cell[4, G7], 1, 0) → H7
  47. If(C8 ≟ Cell[4, E8] ∨ C8 ≟ Cell[4, F8] ∨ C8 ≟ Cell[4, G8], 1, 0) → H8
  48. If(C9 ≟ Cell[4, E9] ∨ C9 ≟ Cell[4, F9] ∨ C9 ≟ Cell[4, G9], 1, 0) → H9
  49. If(C10 ≟ Cell[4, E10] ∨ C10 ≟ Cell[4, F10] ∨ C10 ≟ Cell[4, G10], 1, 0) → H10
  50. If(C11 ≟ Cell[4, E11] ∨ C11 ≟ Cell[4, F11] ∨ C11 ≟ Cell[4, G11], 1, 0) → H11
  51. If(C12 ≟ Cell[4, E12] ∨ C12 ≟ Cell[4, F12] ∨ C12 ≟ Cell[4, G12], 1, 0) → H12
  52. Sum(H1:H12) → H13
  53. Random(1, 10) → u
  54. Polygon(J1, K1, 4) → Polígon18, b_3, c_3, h_3, i_3, D_2, E_2
  55. Polygon(J2, K2, 4) → Polígon19, j_3, k_3, l_3, m_3, F_2, G_2
  56. Polygon(J3, K3, 4) → Polígon20, n_3, p_3, q_3, a_4, H_2, I_2
  57. Polygon(J4, K4, 4) → Polígon21, b_4, c_4, d_4, e_4, J_2, K_2
  58. Polygon(J5, K5, 4) → Polígon22, f_4, g_4, h_4, i_4, L_2, M_2
  59. Polygon(J6, K6, 4) → Polígon23, j_4, k_4, l_4, m_4, N_2, O_2
  60. Polygon(J7, K7, 4) → Polígon24, n_4, p_4, q_4, r_4, P_2, Q_2
  61. Polygon(J8, K8, 4) → Polígon25, a_5, b_5, c_5, d_5, R_2, S_2
  62. Polygon(J9, K9, 4) → Polígon26, e_5, f_5, g_5, h_5, T_2, U_2
  63. Polygon(J10, K10, 4) → Polígon27, i_5, j_5, k_5, l_5, V_2, W_2
  64. Polygon(J11, K11, 4) → Polígon28, m_5, n_5, p_5, q_5, Z_2, A_3
  65. Polygon(J12, K12, 4) → Polígon29, r_5, a_6, b_6, c_6, C_3, D_3
  66. Polygon(B_2, C_2, B_3, E_3) → Polígon30, b_7, c_7, b_8, e_6
  67. Polygon(H_3, I_3, J_3, K_3) → Polígon32, h_6, i_6, j_6, k_6
  68. Polygon(L_3, M_3, N_3, O_3) → Polígon33, l_6, m_6, n_6, o_3
  69. Polygon(P_3, Q_3, R_3, S_3) → Polígon34, p_6, q_6, r_6, s_6
  70. Polygon(T_3, U_3, V_3, W_3) → Polígon35, t_6, u_3, v_3, w_4
  71. Polygon(Z_3, A_4, B_4, C_4) → Polígon36, z_4, a_7, b_{10}, c_9
  72. Polygon(F_3, G_3, D_4, E_4) → Polígon31, f_6, g_6, d_6, e_7
  73. Polygon(F_4, G_4, H_4, I_4) → Polígon37, f_7, g_7, h_7, i_7
  74. Polygon(J_4, K_4, L_4, M_4) → Polígon38, j_7, k_7, l_7, m_7
  75. Polygon(N_4, O_4, P_4, Q_4) → Polígon39, n_7, o_4, p_7, q_7
  76. Polygon(R_4, S_4, T_4, U_4) → Polígon40, r_7, s_7, t_7, u_4
  77. Polygon(V_4, W_4, Z_4, A_5) → Polígon41, v_4, w_5, z_5, a_8
  78. Point(b_7) → B_5
  79. Point(b_8) → C_5
  80. Point(j_6) → E_5
  81. Point(k_7) → H_5
  82. Point(m_7) → I_5
  83. Point(d_6) → J_5
  84. Point(f_6) → K_5
  85. Point(s_6) → M_5
  86. Point(w_4) → N_5
  87. Point(u_3) → O_5
  88. Point(o_4) → Q_5
  89. Point(u_4) → R_5
  90. Point(s_7) → S_5
  91. Point(a_8) → V_5
  92. Point(w_5) → W_5
  93. Point(a_7) → A_6
  94. Polygon(B_2, C_2, B_3, E_3) → Polígon42, b_9, c_8, b_{11}, e_8
  95. Polygon(P_3, S_3, R_3, Q_3) → Polígon43, p_8, s_8, r_8, q_8
  96. Polygon(T_3, W_3, V_3, U_3) → Polígon44, t_8, w_6, v_2, u_2
  97. Polygon(Z_3, C_4, B_4, A_4) → Polígon45, z_6, c_{10}, b_{12}, a_9
  98. Polygon(V_4, A_5, Z_4, W_4) → Polígon46, v_5, a_{10}, z_7, w_7
  99. Polygon(N_4, Q_4, P_4, O_4) → Polígon47, n_8, q_9, p_9, o_1
  100. Polygon(F_3, G_3, D_4, E_4) → Polígon48, f_8, g_8, d_7, e_9
  101. Polygon(H_3, I_3, J_3, K_3) → Polígon49, h_8, i_8, j_8, k_8
  102. Polygon(L_3, M_3, N_3, O_3) → Polígon50, l_8, m_8, n_9, o_2
  103. Polygon(J_4, M_4, L_4, K_4) → Polígon51, j_9, m_9, l_9, k_9
  104. Polygon(R_4, U_4, T_4, S_4) → Polígon52, r_9, u_5, t_9, s_9
  105. Polygon(F_4, I_4, H_4, G_4) → Polígon53, f_9, i_9, h_9, g_9
  106. Segment(B_6, C_6) → d_8
  107. Segment(D_6, E_6) → d_9
  108. Segment(F_6, G_5) → d_{10}
  109. Segment(G_6, H_6) → e_{10}
  110. Segment(I_6, J_6) → f_{10}
  111. Segment(K_6, H_5) → g_{10}
  112. Segment(L_6, M_6) → h_{10}
  113. Segment(N_6, O_6) → i_{10}
  114. Segment(P_6, Q_6) → j_{10}
  115. Segment(R_6, S_6) → k_{10}
  116. Segment(T_6, U_6) → l_{10}
  117. Segment(V_6, W_6) → m_{10}
  118. If(L1 ≟ Cell[13, E1], 1, 0) → N1
  119. If(L2 ≟ Cell[13, E2], 1, 0) → N2
  120. If(L3 ≟ Cell[13, E3], 1, 0) → N3
  121. If(L4 ≟ Cell[13, E4], 1, 0) → N4
  122. If(L5 ≟ Cell[13, E5], 1, 0) → N5
  123. If(L6 ≟ Cell[13, E6], 1, 0) → N6
  124. If(L7 ≟ Cell[13, E7], 1, 0) → N7
  125. If(L8 ≟ Cell[13, E8], 1, 0) → N8
  126. If(L9 ≟ Cell[13, E9], 1, 0) → N9
  127. If(L10 ≟ Cell[13, E10], 1, 0) → N10
  128. If(L11 ≟ Cell[13, E11], 1, 0) → N11
  129. If(L12 ≟ Cell[13, E12], 1, 0) → N12
  130. Sum(N1:N12) → N13
  131. If(R1 ≟ Cell[13, E1], 1, 0) → S1
  132. If(R2 ≟ Cell[13, E2], 1, 0) → S2
  133. If(R3 ≟ Cell[13, E3], 1, 0) → S3
  134. If(R4 ≟ Cell[13, E4], 1, 0) → S4
  135. If(R5 ≟ Cell[13, E5], 1, 0) → S5
  136. If(R6 ≟ Cell[13, E6], 1, 0) → S6
  137. If(R7 ≟ Cell[13, E7], 1, 0) → S7
  138. If(R8 ≟ Cell[13, E8], 1, 0) → S8
  139. If(R9 ≟ Cell[13, E9], 1, 0) → S9
  140. If(R10 ≟ Cell[13, E10], 1, 0) → S10
  141. If(R11 ≟ Cell[13, E11], 1, 0) → S11
  142. If(R12 ≟ Cell[13, E12], 1, 0) → S12
  143. Sum(S1:S12) → S13