分数乘法几何演示 by Lee W Fisher

分数乘法几何演示 by Lee W Fisher
几何画板及绘图内容加载中,请稍等……
2018-09-11 06:05
本范例通过几何面积模型直观演示分数乘法运算。①使用矩形或正方形面积表示分数,将两个分数分别作为长和宽绘制在坐标系中;②核心数学概念为分数乘法运算规则:分子乘分子作为结果的分子,分母乘分母作为结果的分母;③作图要点:利用Polygon命令绘制表示分数的矩形/正方形,用Point命令标记关键点,Segment命令绘制辅助线,Intersect命令找出交点以明确面积区域;④适合小学高年级或初中数学课堂演示,帮助学生建立分数乘法的几何直观理解,也可作为教师教学演示素材。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → q1, a, b, c, d
  2. Point(d) → E
  3. Segment(E, F) → f
  4. Point(d) → G
  5. Segment(G, H) → g
  6. Point(b) → I
  7. Point(d) → J
  8. Segment(I, J) → h
  9. Segment(K, L) → i
  10. Polygon(A_1, B_1, C_1, D_1) → q1_1, a_1, b_1, c_1, d_1
  11. Point(d_1) → E_1
  12. Segment(E_1, F_1) → f_1
  13. Point(d_1) → G_1
  14. Segment(G_1, H_1) → g_1
  15. Point(b_1) → I_1
  16. Point(d_1) → J_1
  17. Segment(I_1, J_1) → h_1
  18. Segment(K_1, L_1) → i_1
  19. Point(d_1) → M
  20. Point(b_1) → N
  21. Segment(M, N) → j
  22. Point(d_1) → O
  23. Segment(O, P) → k
  24. Point(d_1) → Q
  25. Segment(Q, R) → l
  26. Point(d_1) → S
  27. Point(b_1) → T
  28. Segment(S, T) → m
  29. Point(d_1) → U
  30. Point(b_1) → V
  31. Segment(U, V) → n
  32. Point(d_1) → W
  33. Point(b_1) → Z
  34. Segment(W, Z) → p
  35. Point(d_1) → M_1
  36. Segment(M_1, N_1) → q
  37. Point(d_1) → O_1
  38. Segment(O_1, P_1) → r
  39. Point(d_1) → Q_1
  40. Point(b_1) → R_1
  41. Segment(Q_1, R_1) → s
  42. Point(d_1) → S_1
  43. Point(b_1) → T_1
  44. Segment(S_1, T_1) → t
  45. Polygon(A, B, K, L) → q2, a_2, b_2, k_1, l_1
  46. Polygon(A_2, B_2, C_2, D_2) → q1_2, a_3, b_3, c_2, d_2
  47. Point(d_2) → E_2
  48. Segment(E_2, F_2) → f_2
  49. Point(d_2) → G_2
  50. Segment(G_2, H_2) → g_2
  51. Point(b_3) → I_2
  52. Point(d_2) → J_2
  53. Segment(I_2, J_2) → h_2
  54. Segment(K_2, L_2) → i_2
  55. Point(d_2) → M_3
  56. Point(b_3) → N_3
  57. Segment(M_3, N_3) → j_1
  58. Point(d_2) → O_3
  59. Segment(O_3, P_3) → k_2
  60. Point(d_2) → Q_3
  61. Segment(Q_3, R_3) → l_2
  62. Point(d_2) → S_3
  63. Point(b_3) → T_3
  64. Segment(S_3, T_3) → m_1
  65. Point(d_2) → U_1
  66. Point(b_3) → V_1
  67. Segment(U_1, V_1) → n_1
  68. Point(d_2) → W_1
  69. Point(b_3) → Z_1
  70. Segment(W_1, Z_1) → p_1
  71. Point(d_2) → M_2
  72. Segment(M_2, N_2) → q_1
  73. Point(d_2) → O_2
  74. Segment(O_2, P_2) → r_1
  75. Point(d_2) → Q_2
  76. Point(b_3) → R_2
  77. Segment(Q_2, R_2) → s_1
  78. Point(d_2) → S_2
  79. Point(b_3) → T_2
  80. Segment(S_2, T_2) → t_1
  81. Polygon(A_1, B_1, K_1, L_1) → q3, a_4, b_4, k_3, l_3
  82. Polygon(A_2, B_2, P_3, O_3) → q4, a_5, b_5, p_3, o_3
  83. Polygon(E_2, F_2, T_3, S_3) → q5, e_2, f_3, t_3, s_3
  84. Polygon(G_2, H_2, Z_1, W_1) → q6, g_3, h_3, z_1, w_1
  85. Polygon(J_2, O_2, P_2, I_2) → q7, j_2, o_2, p_2, i_3
  86. Polygon(A_2, B_2, K_2, L_2) → q8, a_6, b_6, k_4, l_4
  87. Polygon(A_3, B_3, C_3, D_3) → q1_3, a_7, b_7, c_3, d_3
  88. Point(d_3) → E_3
  89. Segment(E_3, F_3) → f_4
  90. Point(d_3) → G_3
  91. Segment(G_3, H_3) → g_4
  92. Point(b_7) → I_3
  93. Point(d_3) → J_3
  94. Segment(I_3, J_3) → h_4
  95. Segment(K_3, L_3) → i_4
  96. Point(d_3) → M_5
  97. Point(b_7) → N_5
  98. Segment(M_5, N_5) → j_3
  99. Point(d_3) → O_5
  100. Segment(O_5, P_5) → k_5
  101. Point(d_3) → Q_5
  102. Segment(Q_5, R_5) → l_5
  103. Point(d_3) → S_4
  104. Point(b_7) → T_4
  105. Segment(S_4, T_4) → m_2
  106. Point(d_3) → U_2
  107. Point(b_7) → V_2
  108. Segment(U_2, V_2) → n_2
  109. Point(d_3) → W_2
  110. Point(b_7) → Z_2
  111. Segment(W_2, Z_2) → p_4
  112. Point(d_3) → M_4
  113. Segment(M_4, N_4) → q_2
  114. Point(d_3) → O_4
  115. Segment(O_4, P_4) → r_2
  116. Point(d_3) → Q_4
  117. Point(b_7) → R_4
  118. Segment(Q_4, R_4) → s_2
  119. Point(d_3) → S_5
  120. Point(b_7) → T_5
  121. Segment(S_5, T_5) → t_2
  122. Polygon(A_3, B_3, K_3, L_3) → q8_1, a_8, b_8, k_6, l_6
  123. Polygon(A_3, D_3, C_3, B_3) → q9, a_{10}, d_4, c_4, b_{10}
  124. Intersect(a_8, l_6) → U_3
  125. Intersect(a_8, b_8) → V_3
  126. Intersect(p_4, b_8) → W_3
  127. Point(p_4) → Z_3
  128. Polygon(U_3, V_3, W_3, Z_3) → q10, u_3, v_3, w_3, z_3

AI 绘图提示语参考

在坐标系中绘制两个相邻的矩形,分别表示两个分数。第一个矩形由四个顶点构成,内部用线段划分出若干小格,以显示其长度和宽度分别对应分数的分子与分母。第二个矩形与第一个类似,但尺寸不同。在两个矩形之间,再绘制一个由两个矩形的边相交形成的重叠区域,该区域即为两个分数相乘的几何表示。用线段连接关键点,标出各部分的长度和宽度,并突出显示乘积对应的面积区域。整体图形用于直观展示分数乘法的面积模型。
以上提示语为根据原始绘图命令整理而来,仅供参考。