Graphical Multiplication Table

Graphical Multiplication Table
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2014-12-21 04:39
This example uses a graphical method to illustrate a multiplication table, helping students visualize the algebraic forms of various products. It employs GeoGebra commands such as Point, Intersect, and Polygon to demonstrate how multiplication can be represented geometrically. Suitable for students in middle school and above to learn algebraic concepts.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → B
  3. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  4. Point(xAxis) → F
  5. Polygon(A, D, E, F) → poly2, a_1, d_1, e, f
  6. Point(xAxis) → G
  7. Polygon(F, G, H, E) → poly3, f_1, g, h, e_1
  8. Point(xAxis) → I
  9. Polygon(G, I, J, H) → poly4, g_1, i, j, h_1
  10. Point(xAxis) → K
  11. Polygon(I, K, L, J) → poly5, i_1, k, l, j_1
  12. Point(xAxis) → M
  13. Polygon(K, M, N, L) → poly6, k_1, m, n, l_1
  14. Point(xAxis) → O
  15. Polygon(M, O, P, N) → poly7, m_1, o, p, n_1
  16. Point(xAxis) → Q
  17. Polygon(O, Q, R, P) → poly8, o_1, q, r, p_1
  18. Point(xAxis) → S
  19. Polygon(Q, S, T, R) → poly9, q_1, s, t, r_1
  20. Point(xAxis) → U
  21. Polygon(S, U, V, T) → poly10, s_1, u, v, t_1
  22. Point(yAxis) → W
  23. Polygon(C, W, Z, D) → poly11, c_1, w, z, d_2
  24. Point(yAxis) → A_1
  25. Polygon(W, A_1, B_1, Z) → poly12, w_1, a_2, b_1, z_1
  26. Point(yAxis) → C_1
  27. Polygon(A_1, C_1, D_1, B_1) → poly13, a_3, c_2, d_3, b_2
  28. Point(yAxis) → E_1
  29. Polygon(C_1, E_1, F_1, D_1) → poly14, c_3, e_2, f_2, d_4
  30. Point(yAxis) → G_1
  31. Polygon(E_1, G_1, H_1, F_1) → poly15, e_3, g_2, h_2, f_3
  32. Point(yAxis) → I_1
  33. Polygon(G_1, I_1, J_1, H_1) → poly16, g_3, i_2, j_2, h_3
  34. Point(yAxis) → K_1
  35. Polygon(I_1, K_1, L_1, J_1) → poly17, i_3, k_2, l_2, j_3
  36. Point(yAxis) → M_1
  37. Polygon(K_1, M_1, N_1, L_1) → poly18, k_3, m_2, n_2, l_3
  38. Point(yAxis) → O_1
  39. Polygon(M_1, O_1, P_1, N_1) → poly19, m_3, o_2, p_2, n_3
  40. Polygon(D, Z, 4) → poly20, q_2, r_2, s_2, t_2, Q_1, R_1
  41. Polygon(Q_1, S_1, 4) → poly21, b_3, p_3, q_3, r_3, T_1, U_1
  42. Polygon(T_1, V_1, 4) → poly22, s_3, t_3, a_4, b_4, W_1, Z_1
  43. Polygon(W_1, A_2, 4) → poly23, c_4, e_4, f_4, g_4, B_2, C_2
  44. Polygon(B_2, D_2, 4) → poly24, h_4, i_4, j_4, k_4, E_2, F_2
  45. Polygon(E_2, G_2, 4) → poly25, l_4, m_4, n_4, p_4, H_2, I_2
  46. Polygon(H_2, J_2, 4) → poly26, q_4, r_4, s_4, t_4, K_2, L_2
  47. Polygon(K_2, M_2, 4) → poly27, a_5, b_5, c_5, d_5, N_2, O_2
  48. Polygon(N_2, P_2, 4) → poly28, e_5, f_5, g_5, h_5, Q_2, R_2
  49. Polygon(E, Q_1, U_1, H) → poly29, e_6, q_5, u_1, h_6
  50. Polygon(U_1, S_2, J, H) → poly30, u_2, s_5, j_5, h_7
  51. Polygon(S_2, U_1, T_1, Z_1) → poly31, s_6, u_3, t_5, z_2
  52. Polygon(B_1, S_1, Q_1, Z) → poly32, b_6, s_7, q_6, z_3
  53. Polygon(D_1, T_2, S_1, B_1) → poly33, d_6, t_6, s_8, b_7
  54. Polygon(S_1, T_1, V_1, T_2) → poly34, s_9, t_7, v_1, t_8
  55. Polygon(D_1, F_1, U_2, T_2) → poly35, d_7, f_6, u_4, t_9
  56. Polygon(T_2, U_2, V_2, V_1) → poly36, t_{10}, u_5, v_2, v_3
  57. Polygon(V_1, V_2, A_2, W_1) → poly37, v_4, v_5, a_6, w_2
  58. Polygon(F_1, H_1, W_2, U_2) → poly38, f_7, h_8, w_3, u_6
  59. Polygon(U_2, W_2, Z_2, V_2) → poly39, u_7, w_4, z_4, v_6
  60. Polygon(H_1, J_1, A_3, W_2) → poly40, h_9, j_6, a_7, w_5
  61. Polygon(W_2, A_3, B_3, Z_2) → poly41, w_6, a_8, b_8, z_5
  62. Polygon(V_2, Z_2, C_3, A_2) → poly42, v_7, z_6, c_6, a_9
  63. Polygon(A_2, C_3, D_2, B_2) → poly43, a_{10}, c_7, d_8, b_9
  64. Polygon(Z_2, B_3, D_3, C_3) → poly44, z_7, b_{10}, d_9, c_8
  65. Polygon(C_3, D_3, E_3, D_2) → poly45, c_9, d_{10}, e_7, d_{11}
  66. Polygon(D_2, E_3, G_2, E_2) → poly46, d_{12}, e_8, g_6, e_9
  67. Polygon(J_1, L_1, F_3, A_3) → poly47, j_7, l_5, f_8, a_{11}
  68. Polygon(A_3, F_3, G_3, B_3) → poly48, a_{12}, f_9, g_7, b_{11}
  69. Polygon(B_3, G_3, H_3, D_3) → poly49, b_{12}, g_8, h_{10}, d_{13}
  70. Polygon(D_3, H_3, I_3, E_3) → poly50, d_{14}, h_{11}, i_5, e_{10}
  71. Polygon(E_3, I_3, J_3, G_2) → poly51, e_{11}, i_6, j_8, g_9
  72. Polygon(G_2, J_3, J_2, H_2) → poly52, g_{10}, j_9, j_{10}, h_{12}
  73. Polygon(L_1, N_1, K_3, F_3) → poly53, l_6, n_5, k_5, f_{10}
  74. Polygon(F_3, K_3, L_3, G_3) → poly54, f_{11}, k_6, l_7, g_{11}
  75. Polygon(G_3, L_3, M_3, H_3) → poly55, g_{12}, l_8, m_5, h_{13}
  76. Polygon(H_3, M_3, N_3, I_3) → poly56, h_{14}, m_6, n_6, i_7
  77. Polygon(I_3, N_3, O_3, J_3) → poly57, i_8, n_7, o_3, j_{11}
  78. Polygon(J_3, O_3, P_3, J_2) → poly58, j_{12}, o_4, p_5, j_{13}
  79. Polygon(J_2, P_3, M_2, K_2) → poly59, j_{14}, p_6, m_7, k_7
  80. Polygon(N_1, P_1, Q_3, K_3) → poly60, n_8, p_7, q_7, k_8
  81. Polygon(K_3, Q_3, R_3, L_3) → poly61, k_9, q_8, r_5, l_9
  82. Polygon(L_3, R_3, S_3, M_3) → poly62, l_{10}, r_6, s_{10}, m_8
  83. Polygon(M_3, S_3, T_3, N_3) → poly63, m_9, s_{11}, t_{11}, n_9
  84. Polygon(N_3, T_3, U_3, O_3) → poly64, n_{10}, t_{12}, u_8, o_5
  85. Polygon(O_3, U_3, V_3, P_3) → poly65, o_6, u_9, v_8, p_8
  86. Polygon(P_3, V_3, W_3, M_2) → poly66, p_9, v_9, w_7, m_{10}
  87. Polygon(M_2, W_3, P_2, N_2) → poly67, m_{11}, w_8, p_{10}, n_{11}
  88. Polygon(J, S_2, Z_3, L) → poly68, j_{15}, s_{12}, z_8, l_{11}
  89. Polygon(S_2, Z_1, A_4, Z_3) → poly69, s_{13}, z_9, a_{13}, z_{10}
  90. Polygon(Z_1, W_1, C_2, A_4) → poly70, z_{11}, w_9, c_{10}, a_{14}
  91. Polygon(L, Z_3, B_4, N) → poly71, l_{12}, z_{12}, b_{13}, n_{12}
  92. Polygon(Z_3, A_4, C_4, B_4) → poly72, z_{13}, a_{15}, c_{11}, b_{14}
  93. Polygon(A_4, C_2, D_4, C_4) → poly73, a_{16}, c_{12}, d_{15}, c_{13}
  94. Polygon(C_2, B_2, F_2, D_4) → poly74, c_{14}, b_{15}, f_{12}, d_{16}
  95. Polygon(N, B_4, E_4, P) → poly75, n_{13}, b_{16}, e_{12}, p_{11}
  96. Polygon(B_4, C_4, F_4, E_4) → poly76, b_{17}, c_{15}, f_{13}, e_{13}
  97. Polygon(C_4, D_4, G_4, F_4) → poly77, c_{16}, d_{17}, g_{13}, f_{14}
  98. Polygon(D_4, F_2, H_4, G_4) → poly78, d_{18}, f_{15}, h_{15}, g_{14}
  99. Polygon(F_2, E_2, I_2, H_4) → poly79, f_{16}, e_{14}, i_9, h_{16}
  100. Polygon(P, E_4, I_4, R) → poly80, p_{12}, e_{15}, i_{10}, r_7
  101. Polygon(E_4, F_4, J_4, I_4) → poly81, e_{16}, f_{17}, j_{16}, i_{11}
  102. Polygon(F_4, G_4, K_4, J_4) → poly82, f_{18}, g_{15}, k_{10}, j_{17}
  103. Polygon(G_4, H_4, L_4, K_4) → poly83, g_{16}, h_{17}, l_{13}, k_{11}
  104. Polygon(H_4, I_2, M_4, L_4) → poly84, h_{18}, i_{12}, m_{12}, l_{14}
  105. Polygon(I_2, H_2, L_2, M_4) → poly85, i_{13}, h_{19}, l_{15}, m_{13}
  106. Polygon(R, I_4, N_4, T) → poly86, r_8, i_{14}, n_{14}, t_{13}
  107. Polygon(I_4, J_4, O_4, N_4) → poly87, i_{15}, j_{18}, o_7, n_{15}
  108. Polygon(J_4, K_4, P_4, O_4) → poly88, j_{19}, k_{12}, p_{13}, o_8
  109. Polygon(K_4, L_4, Q_4, P_4) → poly89, k_{13}, l_{16}, q_9, p_{14}
  110. Polygon(L_4, M_4, R_4, Q_4) → poly90, l_{17}, m_{14}, r_9, q_{10}
  111. Polygon(M_4, L_2, S_4, R_4) → poly91, m_{15}, l_{18}, s_{14}, r_{10}
  112. Polygon(L_2, K_2, O_2, S_4) → poly92, l_{19}, k_{14}, o_9, s_{15}
  113. Polygon(T, N_4, T_4, V) → poly93, t_{14}, n_{16}, t_{15}, v_{10}
  114. Polygon(N_4, O_4, U_4, T_4) → poly94, n_{17}, o_{10}, u_{10}, t_{16}
  115. Polygon(O_4, P_4, V_4, U_4) → poly95, o_{11}, p_{15}, v_{11}, u_{11}
  116. Polygon(P_4, Q_4, W_4, V_4) → poly96, p_{16}, q_{11}, w_{10}, v_{12}
  117. Polygon(Q_4, R_4, Z_4, W_4) → poly97, q_{12}, r_{11}, z_{14}, w_{11}
  118. Polygon(R_4, S_4, A_5, Z_4) → poly98, r_{12}, s_{16}, a_{17}, z_{15}
  119. Polygon(S_4, O_2, B_5, A_5) → poly99, s_{17}, o_{12}, b_{18}, a_{18}
  120. Polygon(O_2, N_2, R_2, B_5) → poly100, o_{13}, n_{18}, r_{13}, b_{19}

AI Drawing Prompt Reference

Draw a geometric multiplication table with a 10x10 grid of squares, each with a side length of 1, where the bottom-left corner is at the origin. Define rows and columns using a series of points and connect them to form multiple squares and rectangles, illustrating the geometric representation of multiplication.
The prompt above was compiled from the original drawing commands and is for reference only.