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小数乘以10的GeoGebra演示

小数乘以10的GeoGebra演示
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2019-03-15 18:35
函数解析几何几何作图滑块动画函数图像
①这个范例演示了小数0.13乘以10的乘法运算过程及结果变化；②涉及的核心数学概念包括小数乘法、十进制运算、数轴表示；③作图要点——从下方『构造摘要』提炼用到了Segment（线段）、Sequence（数列）、Polygon（多边形）、Join（连接）、Element（元素）、If（条件）、Translate（平移）、Dilate（缩放）、Point（点）、Intersect（交点）、Vector（向量）等GeoGebra命令/对象；④适合初中数学教学，用于帮助学生理解小数乘法运算及数形结合思想。

GeoGebra 命令及参数

  1. Segment(C, D) → f
  2. Segment(D, B) → g
  3. Segment(B, A) → h
  4. Segment(A, C) → i
  5. Segment(F, G) → j
  6. Segment(G, H) → k
  7. Segment(H, E) → l
  8. Segment(E, F) → m
  9. Sequence((k, 17), k, 0, 5) → l1
  10. Sequence((k, 18), k, 0, 5) → l2
  11. Polygon(I, J, K, L) → q1, i_1, j_1, k_1, l_1
  12. Sequence(Polygon[Element[l1, k], Element[l1, k + 1], Element[l2, k + 1], Element[l2, k]], k, 1, 5, 2) → l3
  13. Join({l4, l3}) → l5
  14. Element(l3, 1) → q2
  15. Element(l3, 2) → q3
  16. Element(l3, 3) → q4
  17. Sequence(Element[l1, k], k, 1, 5, 2) → l7
  18. Join({l8, l7}) → l9
  19. Sequence(Vector[Element[l9, k], Element[l6, k]], k, 1, 4) → l10
  20. If(0 < a < 1, Vector[Dilate[Element[l10, 1], a]], Vector[If[a ≥ 1, Vector[Element[l10, 1]]]]) → u
  21. If(1 ≤ a < 2, Vector[Dilate[Element[l10, 2], a - 1]], Vector[If[a ≥ 2, Vector[Element[l10, 2]]]]) → v
  22. If(2 ≤ a < 3, Vector[Dilate[Element[l10, 3], a - 2]], Vector[If[a ≥ 3, Vector[Element[l10, 3]]]]) → w
  23. If(3 ≤ a < 4, Vector[Dilate[Element[l10, 4], a - 3]], Vector[If[a ≥ 4, Vector[Element[l10, 4]]]]) → b
  24. Sequence((0, k), k, 0, 10) → l13
  25. Sequence((10, k), k, 0, 10) → l14
  26. Sequence((12, k), k, 0, 9) → l15
  27. Sequence((13, k), k, 0, 9) → l16
  28. Sequence((14, k), k, 0, 9) → l17
  29. Sequence((15, k), k, 0, 9) → l18
  30. Sequence(Segment[Element[l13, 11 - k], Element[l14, 11 - k]], k, 1, e) → l20
  31. Sequence(Polygon[Element[l13, 12 - k], Element[l13, 11 - k], Element[l14, 11 - k], Element[l14, 12 - k]], k, 1, e) → l19
  32. Translate(Element[l5, 1], Vector[Element[l11, 1]]) → q5
  33. Translate(Element[l5, 2], Vector[Element[l11, 2]]) → q6
  34. Translate(Element[l5, 3], Vector[Element[l11, 3]]) → q7
  35. Translate(Element[l5, 4], Vector[Element[l11, 4]]) → q8
  36. Sequence(Polygon[Element[l15, 12 - k], Element[l15, 11 - k], Element[l16, 11 - k], Element[l16, 12 - k]], k, 1, e) → l12
  37. Sequence(Polygon[Element[l16, 12 - k], Element[l16, 11 - k], Element[l17, 11 - k], Element[l17, 12 - k]], k, 1, e) → l21
  38. Sequence(Polygon[Element[l17, 12 - k], Element[l17, 11 - k], Element[l18, 11 - k], Element[l18, 12 - k]], k, 1, e) → l22
  39. Sequence(Segment[Element[l15, 11 - k], Element[l16, 11 - k]], k, 1, e) → l23
  40. Sequence(Segment[Element[l16, 11 - k], Element[l17, 11 - k]], k, 1, e) → l24
  41. Sequence(Segment[Element[l17, 11 - k], Element[l18, 11 - k]], k, 1, e) → l25
  42. Segment(Q, T) → n
  43. Segment(R, U) → p
  44. Segment(S, V) → q
  45. Dilate(Q, o, Q) → Q'
  46. Dilate(T, o, Q) → T'
  47. Segment(Q', T') → n'
  48. Dilate(R, o, R) → R'
  49. Dilate(U, o, R) → U'
  50. Segment(R', U') → p'
  51. Dilate(S, o, S) → S'
  52. Dilate(V, o, S) → V'
  53. Segment(S', V') → q'
  54. Point(yAxis) → W
  55. Segment(W, Z) → r
  56. Segment(Z, A_1) → s
  57. Point(yAxis) → B_1
  58. Segment(A_1, B_1) → t
  59. Segment(B_1, W) → f_1
  60. Segment(C_1, D_1) → g_1
  61. Segment(D_1, E_1) → h_1
  62. Segment(E_1, F_1) → m_1
  63. Segment(F_1, C_1) → n_1
  64. Segment(G_1, H_1) → p_1
  65. Segment(H_1, I_1) → q_1
  66. Segment(I_1, J_1) → r_1
  67. Segment(J_1, G_1) → s_1
  68. Polygon(A, B, D, C) → q9, a_1, b_1, d_1, c_1
  69. Polygon(F, Q, T, E) → q10, f_2, q_2, t_1, e_1
  70. Polygon(Q, R, U, T) → q11, q_3, r_2, u_1, t_2
  71. Polygon(R, S, V, U) → q12, r_3, s_2, v_1, u_2
  72. Intersect(i_1, l_1) → K_1
  73. Point(i) → L_1
  74. Intersect(j_1, k_1) → M_1
  75. Intersect(f, g) → N_1
  76. Vector(K_1, L_1) → w_1
  77. If(0 < a < 1, Vector[Dilate[w_1, a]]) → v_2
  78. Translate(L, v_2) → L'
  79. Translate(I, v_2) → I'
  80. Segment(L', I') → g_2
  81. Translate(I, v_2) → I'_1
  82. Translate(J, v_2) → J'
  83. Segment(I'_1, J') → h_2
  84. Vector(M_1, N_1) → w_2
  85. If(0 < a < 1, Vector[Dilate[w_2, a]]) → a_2
  86. Translate(J, a_2) → J'_1
  87. Translate(K, a_2) → K'
  88. Segment(J'_1, K') → i_2
  89. Translate(K, a_2) → K'_1
  90. Translate(L, a_2) → L'_1
  91. Segment(K'_1, L'_1) → j_2
  92. Intersect(t, f_1) → O_1
  93. Intersect(r, s) → P_1
  94. Intersect(g_1, n_1) → Q_1
  95. Intersect(h_1, m_1) → R_1
  96. Point(s_1) → S_1
  97. Intersect(p_1, q_1) → T_1
  98. Point(m) → U_1
  99. Point(j) → V_1
  100. Point(j) → Z_1
  101. Point(j) → B_2
  102. Vector(O_1, U_1) → b_2
  103. Vector(P_1, V_1) → c_2
  104. If(1 < a < 2, Vector[Dilate[b_2, a - 1]]) → d_2
  105. Translate(A_1, d_2) → C_2
  106. Translate(B_1, d_2) → D_2
  107. Segment(C_2, D_2) → t'
  108. Translate(B_1, d_2) → E_2
  109. Translate(W, d_2) → W'
  110. Segment(E_2, W') → k_2
  111. If(1 < a ≤ 2, Vector[Dilate[c_2, a - 1]]) → e_2
  112. Translate(W, e_2) → W'_1
  113. Translate(Z, e_2) → Z'
  114. Segment(W'_1, Z') → r'
  115. Translate(Z, e_2) → Z'_1
  116. Translate(A_1, e_2) → F_2
  117. Segment(Z'_1, F_2) → s'
  118. Point(m) → G_2
  119. Segment(G_2, W_1) → l_2
  120. Segment(W_1, V_1) → m_2
  121. Vector(Q_1, W_1) → n_2
  122. Vector(R_1, Z_1) → p_2
  123. If(2 < a < 3, Vector[Dilate[n_2, a - 2]]) → u_3
  124. If(2 < a < 3, Vector[Dilate[p_2, a - 2]]) → v_3
  125. Translate(F_1, u_3) → H_2
  126. Translate(C_1, u_3) → I_2
  127. Segment(H_2, I_2) → f_3
  128. Translate(C_1, u_3) → J_2
  129. Translate(D_1, u_3) → K_2
  130. Segment(J_2, K_2) → g_3
  131. Translate(E_1, v_3) → L_2
  132. Translate(F_1, v_3) → M_2
  133. Segment(L_2, M_2) → h_3
  134. Translate(D_1, v_3) → N_2
  135. Translate(E_1, v_3) → O_2
  136. Segment(N_2, O_2) → i_3
  137. Segment(W_1, A_2) → j_3
  138. Segment(A_2, Z_1) → k_3
  139. Vector(S_1, A_2) → w_3
  140. Vector(T_1, B_2) → a_3
  141. If(3 < a < 4, Vector[Dilate[w_3, a - 3]]) → b_3
  142. If(3 < a < 4, Vector[Dilate[a_3, a - 3]]) → c_3
  143. Translate(J_1, b_3) → P_2
  144. Translate(G_1, b_3) → Q_2
  145. Segment(P_2, Q_2) → l_3
  146. Translate(I_1, b_3) → R_2
  147. Translate(J_1, b_3) → S_2
  148. Segment(R_2, S_2) → m_3
  149. Translate(G_1, c_3) → T_2
  150. Translate(H_1, c_3) → U_2
  151. Segment(T_2, U_2) → n_3
  152. Translate(H_1, c_3) → V_2
  153. Translate(I_1, c_3) → W_2
  154. Segment(V_2, W_2) → p_3