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Dynamic Multiplication Model

Dynamic Multiplication Model
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2014-07-12 18:42
Coordinate GeometrySlider AnimationGraphing
This model is designed for elementary school students or those in teacher education programs to compute different products of decimal numbers. It dynamically demonstrates the multiplication process, involving key concepts of decimal multiplication. Using GeoGebra commands such as Intersect, Point, Polygon, etc., the model allows for dynamic visualization of multiplication. Suitable for high-grade elementary and junior high school students.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Point(yAxis) → D
  4. Polygon(A, B, C, D) → poly1, a, b, c, d
  5. Point(d) → E
  6. Point(b) → F
  7. Segment(E, F) → e
  8. Point(d) → G
  9. Point(b) → H
  10. Segment(G, H) → f
  11. Point(d) → I
  12. Point(b) → J
  13. Segment(I, J) → g
  14. Point(d) → K
  15. Point(b) → L
  16. Segment(K, L) → h
  17. Point(d) → M
  18. Point(b) → N
  19. Segment(M, N) → i
  20. Point(d) → O
  21. Point(b) → P2
  22. Segment(O, P2) → j
  23. Point(d) → Q
  24. Point(b) → R
  25. Segment(Q, R) → k
  26. Point(d) → S
  27. Point(b) → T
  28. Segment(S, T) → l
  29. Point(d) → U
  30. Point(b) → V
  31. Segment(U, V) → m
  32. Point(a) → W
  33. Point(c) → Z
  34. Segment(W, Z) → n
  35. Point(a) → A_1
  36. Point(c) → B_1
  37. Segment(A_1, B_1) → p
  38. Point(a) → C_1
  39. Point(c) → D_1
  40. Segment(C_1, D_1) → q
  41. Point(a) → E_1
  42. Point(c) → F_1
  43. Segment(E_1, F_1) → r
  44. Point(a) → G_1
  45. Point(c) → H_1
  46. Segment(G_1, H_1) → s
  47. Point(a) → I_1
  48. Point(c) → J_1
  49. Segment(I_1, J_1) → t
  50. Point(c) → L_1
  51. Segment(K_1, L_1) → a_1
  52. Point(a) → M_1
  53. Segment(M_1, N_1) → b_1
  54. Point(a) → O_1
  55. Point(c) → P_1
  56. Segment(O_1, P_1) → c_1
  57. Segment(A, P) → d_1
  58. OrthogonalLine(P, a) → e_1
  59. OrthogonalLine(P, d) → f_1
  60. Intersect(e_1, a) → Q_1
  61. Intersect(f_1, d) → R_1
  62. Polygon(A, Q_1, P, R_1) → poly2, a_2, q_1, p_1, r_1
  63. Product({α, β}) → v
  64. Intersect(b, a) → S_1
  65. Segment(A, S_1) → g_1
  66. Polygon(P, R_1, A, Q_1) → poly3, p_2, r_2, a_3, q_2
  67. Intersect(f, n) → T_1
  68. Circle(T_1, 0.2) → h_1
  69. Intersect(f, p) → U_1
  70. Circle(U_1, 0.2) → k_1
  71. Intersect(f, q) → V_1
  72. Circle(V_1, 0.2) → s_1
  73. Intersect(f, r) → W_1
  74. Circle(W_1, 0.2) → t_1
  75. Intersect(f, s) → Z_1
  76. Circle(Z_1, 0.2) → c_2
  77. Intersect(f, t) → A_2
  78. Circle(A_2, 0.2) → d_2
  79. Intersect(f, b_1) → C_2
  80. Circle(C_2, 0.2) → f_2
  81. Intersect(f, c_1) → D_2
  82. Circle(D_2, 0.2) → g_2
  83. Intersect(b, f) → E_2
  84. Circle(E_2, 0.2) → h_2
  85. Intersect(b, e) → F_2
  86. Circle(F_2, 0.2) → k_2
  87. Intersect(e, c_1) → G_2
  88. Circle(G_2, 0.2) → s_2
  89. Intersect(e, b_1) → H_2
  90. Circle(H_2, 0.2) → t_2
  91. Point(t) → J_2
  92. Circle(J_2, 0.2) → d_3
  93. Intersect(e, s) → K_2
  94. Circle(K_2, 0.2) → e_3
  95. Intersect(e, r) → L_2
  96. Circle(L_2, 0.2) → f_3
  97. Intersect(e, q) → M_2
  98. Circle(M_2, 0.2) → g_3
  99. Intersect(e, p) → N_2
  100. Circle(N_2, 0.2) → h_3
  101. Intersect(e, n) → O_2
  102. Circle(O_2, 0.2) → k_3
  103. Intersect(g, n) → P_2
  104. Circle(P_2, 0.2) → p_3
  105. Intersect(g, p) → Q_2
  106. Circle(Q_2, 0.2) → q_3
  107. Intersect(g, q) → R_2
  108. Circle(R_2, 0.2) → r_3
  109. Intersect(g, r) → S_2
  110. Circle(S_2, 0.2) → s_3
  111. Intersect(g, s) → T_2
  112. Circle(T_2, 0.2) → t_3
  113. Intersect(g, t) → U_2
  114. Circle(U_2, 0.2) → c_4
  115. Intersect(g, b_1) → W_2
  116. Circle(W_2, 0.2) → e_4
  117. Intersect(g, c_1) → Z_2
  118. Circle(Z_2, 0.2) → f_4
  119. Intersect(b, g) → A_3
  120. Circle(A_3, 0.2) → g_4
  121. Intersect(b, h) → B_3
  122. Circle(B_3, 0.2) → h_4
  123. Intersect(h, c_1) → C_3
  124. Circle(C_3, 0.2) → k_4
  125. Intersect(h, b_1) → D_3
  126. Circle(D_3, 0.2) → p_4
  127. Intersect(h, t) → F_3
  128. Circle(F_3, 0.2) → r_4
  129. Intersect(h, s) → G_3
  130. Circle(G_3, 0.2) → s_4
  131. Intersect(h, r) → H_3
  132. Circle(H_3, 0.2) → t_4
  133. Intersect(h, q) → I_3
  134. Circle(I_3, 0.2) → c_5
  135. Intersect(h, p) → J_3
  136. Circle(J_3, 0.2) → d_5
  137. Intersect(h, n) → K_3
  138. Circle(K_3, 0.2) → e_5
  139. Intersect(i, n) → L_3
  140. Circle(L_3, 0.2) → f_5
  141. Intersect(i, p) → M_3
  142. Circle(M_3, 0.2) → g_5
  143. Intersect(i, q) → N_3
  144. Circle(N_3, 0.2) → h_5
  145. Intersect(i, r) → O_3
  146. Circle(O_3, 0.2) → k_5
  147. Intersect(i, s) → P_3
  148. Circle(P_3, 0.2) → p_5
  149. Intersect(i, t) → Q_3
  150. Circle(Q_3, 0.2) → q_5
  151. Intersect(i, a_1) → R_3
  152. Circle(R_3, 0.2) → r_5
  153. Intersect(i, b_1) → S_3
  154. Circle(S_3, 0.2) → s_5
  155. Intersect(i, c_1) → T_3
  156. Circle(T_3, 0.2) → t_5
  157. Intersect(b, i) → U_3
  158. Circle(U_3, 0.2) → c_6
  159. Intersect(e, a_1) → B_2
  160. Circle(B_2, 0.2) → e_2
  161. Intersect(f, a_1) → I_2
  162. Circle(I_2, 0.2) → c_3
  163. Intersect(g, a_1) → V_2
  164. Circle(V_2, 0.2) → d_4
  165. Intersect(h, a_1) → E_3
  166. Circle(E_3, 0.2) → q_4
  167. Intersect(j, n) → V_3
  168. Circle(V_3, 0.2) → d_6
  169. Intersect(j, p) → W_3
  170. Circle(W_3, 0.2) → e_6
  171. Intersect(j, q) → Z_3
  172. Circle(Z_3, 0.2) → f_6
  173. Intersect(j, r) → A_4
  174. Circle(A_4, 0.2) → g_6
  175. Intersect(j, s) → B_4
  176. Circle(B_4, 0.2) → h_6
  177. Intersect(j, t) → C_4
  178. Circle(C_4, 0.2) → k_6
  179. Intersect(j, a_1) → D_4
  180. Circle(D_4, 0.2) → p_6
  181. Intersect(j, b_1) → E_4
  182. Circle(E_4, 0.2) → q_6
  183. Intersect(j, c_1) → F_4
  184. Circle(F_4, 0.2) → r_6
  185. Intersect(b, j) → G_4
  186. Circle(G_4, 0.2) → s_6
  187. Intersect(b, k) → H_4
  188. Circle(H_4, 0.2) → t_6
  189. Intersect(k, c_1) → I_4
  190. Circle(I_4, 0.2) → c_7
  191. Intersect(k, b_1) → J_4
  192. Circle(J_4, 0.2) → d_7
  193. Intersect(k, a_1) → K_4
  194. Circle(K_4, 0.2) → e_7
  195. Intersect(k, t) → L_4
  196. Circle(L_4, 0.2) → f_7
  197. Intersect(k, s) → M_4
  198. Circle(M_4, 0.2) → g_7
  199. Intersect(k, r) → N_4
  200. Circle(N_4, 0.2) → h_7
  201. Intersect(k, q) → O_4
  202. Circle(O_4, 0.2) → k_7
  203. Intersect(k, p) → P_4
  204. Circle(P_4, 0.2) → p_7
  205. Intersect(k, n) → Q_4
  206. Circle(Q_4, 0.2) → q_7
  207. Intersect(l, n) → R_4
  208. Circle(R_4, 0.2) → r_7
  209. Intersect(l, p) → S_4
  210. Circle(S_4, 0.2) → s_7
  211. Intersect(l, q) → T_4
  212. Circle(T_4, 0.2) → t_7
  213. Intersect(l, r) → U_4
  214. Circle(U_4, 0.2) → c_8
  215. Intersect(l, s) → V_4
  216. Circle(V_4, 0.2) → d_8
  217. Intersect(l, t) → W_4
  218. Circle(W_4, 0.2) → e_8
  219. Intersect(l, a_1) → Z_4
  220. Circle(Z_4, 0.2) → f_8
  221. Intersect(l, b_1) → A_5
  222. Circle(A_5, 0.2) → g_8
  223. Intersect(l, c_1) → B_5
  224. Circle(B_5, 0.2) → h_8
  225. Intersect(b, l) → C_5
  226. Circle(C_5, 0.2) → k_8
  227. Intersect(b, m) → D_5
  228. Circle(D_5, 0.2) → p_8
  229. Intersect(m, c_1) → E_5
  230. Circle(E_5, 0.2) → q_8
  231. Intersect(m, b_1) → F_5
  232. Circle(F_5, 0.2) → r_8
  233. Intersect(m, a_1) → G_5
  234. Circle(G_5, 0.2) → s_8
  235. Intersect(m, t) → H_5
  236. Circle(H_5, 0.2) → t_8
  237. Intersect(m, s) → I_5
  238. Circle(I_5, 0.2) → c_9
  239. Intersect(m, r) → J_5
  240. Circle(J_5, 0.2) → d_9
  241. Intersect(m, q) → K_5
  242. Circle(K_5, 0.2) → e_9
  243. Intersect(m, p) → L_5
  244. Circle(L_5, 0.2) → f_9
  245. Intersect(m, n) → M_5
  246. Circle(M_5, 0.2) → g_9
  247. Intersect(c, n) → N_5
  248. Circle(N_5, 0.2) → h_9
  249. Intersect(c, p) → O_5
  250. Circle(O_5, 0.2) → k_9
  251. Intersect(c, q) → P_5
  252. Circle(P_5, 0.2) → p_9
  253. Intersect(c, r) → Q_5
  254. Circle(Q_5, 0.2) → q_9
  255. Intersect(c, s) → R_5
  256. Circle(R_5, 0.2) → r_9
  257. Intersect(c, t) → S_5
  258. Circle(S_5, 0.2) → s_9
  259. Intersect(c, a_1) → T_5
  260. Circle(T_5, 0.2) → t_9
  261. Intersect(c, b_1) → U_5
  262. Circle(U_5, 0.2) → c_{10}
  263. Intersect(c, c_1) → V_5
  264. Circle(V_5, 0.2) → d_{10}
  265. Intersect(c, b) → W_5
  266. Circle(W_5, 0.2) → e_{10}

AI Drawing Prompt Reference

Draw a coordinate system with the intersection point A of the x-axis and y-axis, and points B on the x-axis and D on the y-axis. Use these four points to draw a rectangle poly1. Then, take points E, F, G, H, I, J, K, L, M, N, O, P2, Q, R, S, T, U, V on the x-axis and y-axis respectively, and draw a series of parallel line segments to form a dynamic multiplication model to demonstrate the process of decimal multiplication.
The prompt above was compiled from the original drawing commands and is for reference only.