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重复加法演示乘法：可视化乘法本质

重复加法演示乘法：可视化乘法本质
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2020-07-21 17:14
多边形向量函数变换滑块动画
① 本范例通过将多个相同图片（如苹果或方块）重复平移排列，直观展示“乘法即重复加法”的数学现象，帮助学习者从视觉上理解乘法的意义。② 核心数学概念包括乘法与加法的关系、整数倍、向量平移以及简单的计数与求和。③ 作图要点：使用GeoGebra的Vector（向量）和Translate（平移）命令将图片对象（pic1、pic2等）按指定向量复制多次，配合Random（随机）生成不同数量的对象，Polygon（多边形）构建背景框架，Textfield（文本框）输入乘数与被乘数，If（条件判断）控制显示逻辑，最终通过按钮（button1）触发动态演示。④ 适合小学中高年级或初中起始阶段学习乘法概念，也可用于教师课堂演示，帮助学生建立从加法到乘法的抽象思维过渡。

GeoGebra 命令及参数

  1. Vector(A, C) → u
  2. Translate(pic1, u) → pic1'
  3. Translate(pic1', u) → pic1''
  4. Translate(pic1, u) → pic1'_1
  5. Translate(pic1'', u) → pic1'''
  6. Translate(pic1''', Vector[(0.019999999999999574, 0)]) → pic2
  7. Translate(pic2, u) → pic2'
  8. Vector(A, D) → v
  9. Translate(pic1, v) → pic1'_2
  10. Translate(pic1'_1, v) → pic3
  11. Translate(pic1'', v) → pic1'''_1
  12. Translate(pic2, v) → pic2'_1
  13. Translate(pic2', v) → pic2''
  14. Random(0, 10) → a
  15. Random(0, 10) → b
  16. Translate(pic4, Vector[(0.020000000000000018, 0.040000000000000036)]) → pic4'
  17. Translate(pic4', u) → pic4''
  18. Translate(pic4'', u) → pic4'''
  19. Translate(pic4''', u) → pic5
  20. Translate(pic5, u) → pic5'
  21. Translate(pic4', v) → pic4''_1
  22. Translate(pic4''_1, u) → pic6
  23. Translate(pic6, u) → pic6'
  24. Translate(pic6', u) → pic6''
  25. Translate(pic6'', Vector[(0, 0.040000000000000036)]) → pic6'''
  26. Translate(pic6''', u) → pic7
  27. Translate(pic8, u) → pic8'
  28. Translate(pic8', u) → pic8''
  29. Translate(pic8'', u) → pic8'''
  30. Translate(pic8''', u) → pic9
  31. Translate(pic8, v) → pic8'_1
  32. Translate(pic8', v) → pic8''_1
  33. Translate(pic8'', v) → pic8'''_1
  34. Translate(pic8''', v) → pic10
  35. Translate(pic9, v) → pic9'
  36. Translate(C, Vector[(0.26000000000000045, -0.08000000000000007)]) → C'
  37. Translate(pic11, u) → pic11'
  38. Translate(pic11', u) → pic11''
  39. Translate(pic11'', u) → pic11'''
  40. Translate(pic11''', u) → pic12
  41. Translate(pic11, v) → pic11'_1
  42. Translate(pic11'_1, u) → pic13
  43. Translate(pic13, u) → pic13'
  44. Translate(pic13', u) → pic13''
  45. Translate(pic13'', u) → pic13'''
  46. Translate(pic14, u) → pic14'
  47. Translate(pic14', u) → pic14''
  48. Translate(pic14'', u) → pic14'''
  49. Translate(pic14''', u) → pic15
  50. Translate(pic14, v) → pic14'_1
  51. Translate(pic14'_1, u) → pic16
  52. Translate(pic16, u) → pic16'
  53. Translate(pic16', u) → pic16''
  54. Translate(pic16'', u) → pic16'''
  55. Translate(pic17, Vector[(-0.020000000000000018, 0.019999999999999574)]) → pic17'
  56. Translate(pic17', u) → pic17''
  57. Translate(pic17'', u) → pic17'''
  58. Translate(pic17''', u) → pic18
  59. Translate(pic18, u) → pic18'
  60. Translate(pic17', v) → pic17''_1
  61. Translate(pic17''_1, u) → pic19
  62. Translate(pic19, u) → pic19'
  63. Translate(pic19', u) → pic19''
  64. Translate(pic19'', u) → pic19'''
  65. Translate(pic20, u) → pic20'
  66. Translate(pic20', u) → pic20''
  67. Translate(pic20'', u) → pic20'''
  68. Translate(pic20''', u) → pic21
  69. Translate(pic20, v) → pic20'_1
  70. Translate(pic20'_1, u) → pic22
  71. Translate(pic22, u) → pic22'
  72. Translate(pic22', Vector[(0.040000000000000036, 0)]) → pic22''
  73. Translate(pic22', Vector[(0.040000000000000036, 0.04)]) → pic22''_1
  74. Translate(pic22, u) → pic22'_1
  75. Translate(pic22'_1, u) → pic23
  76. Translate(pic23, u) → pic23'
  77. Translate(pic24, u) → pic24'
  78. Translate(pic24', u) → pic24''
  79. Translate(pic24'', u) → pic24'''
  80. Translate(pic24''', u) → pic25
  81. Translate(pic24, v) → pic24'_1
  82. Translate(pic24'_1, u) → pic26
  83. Translate(pic26, u) → pic26'
  84. Translate(pic26', u) → pic26''
  85. Translate(pic26'', u) → pic26'''
  86. Translate(pic27, u) → pic27'
  87. Translate(pic27', u) → pic27''
  88. Translate(pic27'', u) → pic27'''
  89. Translate(pic27''', u) → pic28
  90. Translate(pic27, v) → pic27'_1
  91. Translate(pic27'_1, Vector[(0, -0.020000000000000018)]) → pic29
  92. Translate(pic29, u) → pic29'
  93. Vector(A_1, P) → w
  94. Translate(pic29', w) → pic29''
  95. Translate(pic29', Vector[(3.040000000000001, 0)]) → pic29''_1
  96. Translate(pic29''_1, u) → pic30
  97. Translate(pic30, u) → pic30'
  98. Translate(pic32, u) → pic32'
  99. Translate(pic32', u) → pic32''
  100. Translate(pic32'', u) → pic32'''
  101. Translate(pic32''', u) → pic31
  102. Translate(pic32, v) → pic32'_1
  103. Translate(pic32'_1, u) → pic33
  104. Translate(pic33, u) → pic33'
  105. Translate(pic33', Vector[(0.020000000000000018, 0)]) → pic33''
  106. Translate(pic33', Vector[(0.020000000000000018, 0)]) → pic33''_1
  107. Translate(pic33', Vector[(0, 0)]) → pic33''_2
  108. Translate(pic33', u) → pic33''_3
  109. Translate(pic33''_3, Vector[(0.040000000000000036, 0.020000000000000018)]) → pic34
  110. Translate(pic33', u) → pic33''_4
  111. Translate(pic33''_4, u) → pic35
  112. Polygon(G_1, H_1, J_1, I_1) → q1, g_1, h_1, j_1, i_1
  113. Translate(G_1, u) → K_1
  114. Translate(H_1, u) → L_1
  115. Translate(J_1, u) → M_1
  116. Translate(I_1, u) → N_1
  117. Polygon(K_1, L_1, M_1, N_1) → q1', k_1, l_1, m_1, n_1
  118. Translate(K_1, u) → O_1
  119. Translate(L_1, u) → P_1
  120. Translate(M_1, u) → Q_1
  121. Translate(N_1, u) → R_1
  122. Polygon(O_1, P_1, Q_1, R_1) → q1'', o_1, p_1, q_1, r_1
  123. Translate(O_1, u) → S_1
  124. Translate(P_1, u) → T_1
  125. Translate(Q_1, u) → U_1
  126. Translate(R_1, u) → V_1
  127. Polygon(S_1, T_1, U_1, V_1) → q1''', s_1, t_1, u_1, v_1
  128. Translate(S_1, u) → W_1
  129. Translate(T_1, u) → Z_1
  130. Translate(U_1, u) → A_2
  131. Translate(V_1, u) → B_2
  132. Polygon(W_1, Z_1, A_2, B_2) → q2, w_1, z_1, a_2, b_2
  133. Vector(G_1, I_1) → c
  134. Translate(G_1, c) → C_2
  135. Translate(H_1, c) → D_2
  136. Translate(J_1, c) → E_2
  137. Translate(I_1, c) → F_2
  138. Polygon(C_2, D_2, E_2, F_2) → q1'_1, c_2, d_2, e_2, f_2
  139. Translate(C_2, u) → G_2
  140. Translate(D_2, u) → H_2
  141. Translate(E_2, u) → I_2
  142. Translate(F_2, u) → J_2
  143. Polygon(G_2, H_2, I_2, J_2) → q3, g_2, h_2, i_2, j_2
  144. Translate(G_2, u) → K_2
  145. Translate(H_2, u) → L_2
  146. Translate(I_2, u) → M_2
  147. Translate(J_2, u) → N_2
  148. Polygon(K_2, L_2, M_2, N_2) → q3', k_2, l_2, m_2, n_2
  149. Translate(K_2, u) → O_2
  150. Translate(L_2, u) → P_2
  151. Translate(M_2, u) → Q_2
  152. Translate(N_2, u) → R_2
  153. Polygon(O_2, P_2, Q_2, R_2) → q3'', o_2, p_2, q_2, r_2
  154. Translate(O_2, u) → S_2
  155. Translate(P_2, u) → T_2
  156. Translate(Q_2, u) → U_2
  157. Translate(R_2, u) → V_2
  158. Polygon(S_2, T_2, U_2, V_2) → q3''', s_2, t_2, u_2, v_2
  159. Random(0, 10) → a_1
  160. Random(0, 10) → a_3
  161. Random(0, 10) → a_4
  162. Random(0, 10) → a_5
  163. Random(0, 10) → a_6
  164. Random(0, 10) → a_7
  165. Textfield(e) → InputBox1
  166. If(e ≟ text14, text15, text16) → text17
  167. If(e ≟ text14, pic37, pic36) → pic38

AI 绘图提示语参考

在画布上放置一组相同的小图标（如苹果或方块），通过沿水平方向重复平移复制，形成一排等间距的图案，表示乘法中的重复相加。再沿垂直方向平移整排图案，生成多行，构成矩形阵列。每行数量相同，行数由乘数决定。用浅色多边形框出整个阵列区域，并在旁边设置输入框和按钮，用于调整乘数与被乘数，动态改变阵列的规模。整体布局清晰，突出乘法与加法之间的对应关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。