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Integer Multiplication Game

Integer Multiplication Game
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2015-05-26 01:17
Geometric ConstructionSlider Animation
In collections Introduction to Integers and Integer Arithmetics Introduction to Integers and Integer Arithmetics
This example is an interactive applet demonstrating integer multiplication for students. It involves core math concepts like integer operations, geometric transformations, and random number generation. The construction uses commands such as RandomElement, Polygon, Point, Rotate, Midpoint, and Segment. Suitable for elementary or middle school students for practice and gamified learning.

GeoGebra Commands & Parameters

  1. RandomElement({-3, -2, -1, 1, 2, 3}) → r1
  2. Polygon(A, B, C, D) → poly1, a, b, c, d
  3. Point(Circle[E, a]) → F
  4. Rotate(F + (b, 0), Angle[C - B] + Angle[F - E] - Angle[B - A], F) → G
  5. Rotate(G + (c, 0), Angle[D - C] + Angle[G - F] - Angle[C - B], G) → H
  6. Polygon(E, F, G, H) → poly2, e, f, g, h
  7. Point(Circle[I, e]) → J
  8. Rotate(J + (f, 0), Angle[G - F] + Angle[J - I] - Angle[F - E], J) → K
  9. Rotate(K + (g, 0), Angle[H - G] + Angle[K - J] - Angle[G - F], K) → L
  10. Polygon(I, J, K, L) → poly3, i, j, k, l
  11. Point(Circle[M, i]) → N
  12. Rotate(N + (j, 0), Angle[K - J] + Angle[N - M] - Angle[J - I], N) → O
  13. Rotate(O + (k, 0), Angle[L - K] + Angle[O - N] - Angle[K - J], O) → P
  14. Polygon(M, N, O, P) → poly4, m, n, o, p
  15. Point(Circle[Q, a]) → R
  16. Rotate(R + (b, 0), Angle[C - B] + Angle[R - Q] - Angle[B - A], R) → S
  17. Rotate(S + (c, 0), Angle[D - C] + Angle[S - R] - Angle[C - B], S) → T
  18. Polygon(Q, R, S, T) → poly5, q, r, s, t
  19. Point(Circle[U, e]) → V
  20. Rotate(V + (f, 0), Angle[G - F] + Angle[V - U] - Angle[F - E], V) → W
  21. Rotate(W + (g, 0), Angle[H - G] + Angle[W - V] - Angle[G - F], W) → Z
  22. Polygon(U, V, W, Z) → poly6, u, v, w, z_1
  23. Point(Circle[A_1, i]) → B_1
  24. Rotate(B_1 + (j, 0), Angle[K - J] + Angle[B_1 - A_1] - Angle[J - I], B_1) → C_1
  25. Rotate(C_1 + (k, 0), Angle[L - K] + Angle[C_1 - B_1] - Angle[K - J], C_1) → D_1
  26. Polygon(A_1, B_1, C_1, D_1) → poly7, a_1, b_1, c_1, d_1
  27. Point(Circle[E_1, m]) → F_1
  28. Rotate(F_1 + (n, 0), Angle[O - N] + Angle[F_1 - E_1] - Angle[N - M], F_1) → G_1
  29. Rotate(G_1 + (o, 0), Angle[P - O] + Angle[G_1 - F_1] - Angle[O - N], G_1) → H_1
  30. Polygon(E_1, F_1, G_1, H_1) → poly8, e_1, f_1, g_1, h_1
  31. Point(Circle[I_1, q]) → J_1
  32. Rotate(J_1 + (r, 0), Angle[S - R] + Angle[J_1 - I_1] - Angle[R - Q], J_1) → K_1
  33. Rotate(K_1 + (s, 0), Angle[T - S] + Angle[K_1 - J_1] - Angle[S - R], K_1) → L_1
  34. Polygon(I_1, J_1, K_1, L_1) → poly9, i_1, j_1, k_1, l_1
  35. Point(Circle[N_1, a]) → O_1
  36. Rotate(O_1 + (b, 0), Angle[C - B] + Angle[O_1 - N_1] - Angle[B - A], O_1) → P_1
  37. Rotate(P_1 + (c, 0), Angle[D - C] + Angle[P_1 - O_1] - Angle[C - B], P_1) → Q_1
  38. Polygon(N_1, O_1, P_1, Q_1) → poly10, n_1, o_1, p_1, q_1
  39. Point(Circle[R_1, e]) → S_1
  40. Rotate(S_1 + (f, 0), Angle[G - F] + Angle[S_1 - R_1] - Angle[F - E], S_1) → T_1
  41. Rotate(T_1 + (g, 0), Angle[H - G] + Angle[T_1 - S_1] - Angle[G - F], T_1) → U_1
  42. Polygon(R_1, S_1, T_1, U_1) → poly11, r_1, s_1, t_1, u_1
  43. Point(Circle[V_1, i]) → W_1
  44. Rotate(W_1 + (j, 0), Angle[K - J] + Angle[W_1 - V_1] - Angle[J - I], W_1) → Z_1
  45. Rotate(Z_1 + (k, 0), Angle[L - K] + Angle[Z_1 - W_1] - Angle[K - J], Z_1) → A_2
  46. Polygon(V_1, W_1, Z_1, A_2) → poly12, v_1, w_1, z_2, a_2
  47. Point(Circle[B_2, m]) → C_2
  48. Rotate(C_2 + (n, 0), Angle[O - N] + Angle[C_2 - B_2] - Angle[N - M], C_2) → D_2
  49. Rotate(D_2 + (o, 0), Angle[P - O] + Angle[D_2 - C_2] - Angle[O - N], D_2) → E_2
  50. Polygon(B_2, C_2, D_2, E_2) → poly13, b_2, c_2, d_2, e_2
  51. Point(Circle[F_2, q]) → G_2
  52. Rotate(G_2 + (r, 0), Angle[S - R] + Angle[G_2 - F_2] - Angle[R - Q], G_2) → H_2
  53. Rotate(H_2 + (s, 0), Angle[T - S] + Angle[H_2 - G_2] - Angle[S - R], H_2) → I_2
  54. Polygon(F_2, G_2, H_2, I_2) → poly14, f_2, g_2, h_2, i_2
  55. Point(Circle[J_2, u]) → K_2
  56. Rotate(K_2 + (v, 0), Angle[W - V] + Angle[K_2 - J_2] - Angle[V - U], K_2) → L_2
  57. Rotate(L_2 + (w, 0), Angle[Z - W] + Angle[L_2 - K_2] - Angle[W - V], L_2) → M_2
  58. Polygon(J_2, K_2, L_2, M_2) → poly15, j_2, k_2, l_2, m_2
  59. Point(Circle[N_2, a_1]) → O_2
  60. Rotate(O_2 + (b_1, 0), Angle[C_1 - B_1] + Angle[O_2 - N_2] - Angle[B_1 - A_1], O_2) → P_2
  61. Rotate(P_2 + (c_1, 0), Angle[D_1 - C_1] + Angle[P_2 - O_2] - Angle[C_1 - B_1], P_2) → Q_2
  62. Polygon(N_2, O_2, P_2, Q_2) → poly16, n_2, o_2, p_2, q_2
  63. Point(Circle[R_2, e_1]) → S_2
  64. Rotate(S_2 + (f_1, 0), Angle[G_1 - F_1] + Angle[S_2 - R_2] - Angle[F_1 - E_1], S_2) → T_2
  65. Rotate(T_2 + (g_1, 0), Angle[H_1 - G_1] + Angle[T_2 - S_2] - Angle[G_1 - F_1], T_2) → U_2
  66. Polygon(R_2, S_2, T_2, U_2) → poly17, r_2, s_2, t_2, u_2
  67. Point(Circle[V_2, i_1]) → W_2
  68. Rotate(W_2 + (j_1, 0), Angle[K_1 - J_1] + Angle[W_2 - V_2] - Angle[J_1 - I_1], W_2) → Z_2
  69. Rotate(Z_2 + (k_1, 0), Angle[L_1 - K_1] + Angle[Z_2 - W_2] - Angle[K_1 - J_1], Z_2) → A_3
  70. Polygon(V_2, W_2, Z_2, A_3) → poly18, v_2, w_2, z_3, a_3
  71. Point(Circle[M_1, b_2]) → B_3
  72. Rotate(B_3 + (c_2, 0), Angle[D_2 - C_2] + Angle[B_3 - M_1] - Angle[C_2 - B_2], B_3) → C_3
  73. Rotate(C_3 + (d_2, 0), Angle[E_2 - D_2] + Angle[C_3 - B_3] - Angle[D_2 - C_2], C_3) → D_3
  74. Polygon(M_1, B_3, C_3, D_3) → poly19, m_1, b_3, c_3, d_3
  75. Point(Circle[E_3, v_1]) → F_3
  76. Rotate(F_3 + (w_1, 0), Angle[Z_1 - W_1] + Angle[F_3 - E_3] - Angle[W_1 - V_1], F_3) → G_3
  77. Rotate(G_3 + (z_2, 0), Angle[A_2 - Z_1] + Angle[G_3 - F_3] - Angle[Z_1 - W_1], G_3) → H_3
  78. Polygon(E_3, F_3, G_3, H_3) → poly20, e_3, f_3, g_3, h_3
  79. Point(Circle[I_3, f_2]) → J_3
  80. Rotate(J_3 + (g_2, 0), Angle[H_2 - G_2] + Angle[J_3 - I_3] - Angle[G_2 - F_2], J_3) → K_3
  81. Rotate(K_3 + (h_2, 0), Angle[I_2 - H_2] + Angle[K_3 - J_3] - Angle[H_2 - G_2], K_3) → L_3
  82. Polygon(I_3, J_3, K_3, L_3) → poly21, i_3, j_3, k_3, l_3
  83. Point(Circle[M_3, j_2]) → N_3
  84. Rotate(N_3 + (k_2, 0), Angle[L_2 - K_2] + Angle[N_3 - M_3] - Angle[K_2 - J_2], N_3) → O_3
  85. Rotate(O_3 + (l_2, 0), Angle[M_2 - L_2] + Angle[O_3 - N_3] - Angle[L_2 - K_2], O_3) → P_3
  86. Polygon(M_3, N_3, O_3, P_3) → poly22, m_3, n_3, o_3, p_3
  87. Point(Circle[Q_3, n_2]) → R_3
  88. Rotate(R_3 + (o_2, 0), Angle[P_2 - O_2] + Angle[R_3 - Q_3] - Angle[O_2 - N_2], R_3) → S_3
  89. Rotate(S_3 + (p_2, 0), Angle[Q_2 - P_2] + Angle[S_3 - R_3] - Angle[P_2 - O_2], S_3) → T_3
  90. Polygon(Q_3, R_3, S_3, T_3) → poly23, q_3, r_3, s_3, t_3
  91. Point(Circle[U_3, r_2]) → V_3
  92. Rotate(V_3 + (s_2, 0), Angle[T_2 - S_2] + Angle[V_3 - U_3] - Angle[S_2 - R_2], V_3) → W_3
  93. Rotate(W_3 + (t_2, 0), Angle[U_2 - T_2] + Angle[W_3 - V_3] - Angle[T_2 - S_2], W_3) → Z_3
  94. Polygon(U_3, V_3, W_3, Z_3) → poly24, u_3, v_3, w_3, z_4
  95. Point(Circle[A_4, a]) → B_4
  96. Rotate(B_4 + (b, 0), Angle[C - B] + Angle[B_4 - A_4] - Angle[B - A], B_4) → C_4
  97. Rotate(C_4 + (c, 0), Angle[D - C] + Angle[C_4 - B_4] - Angle[C - B], C_4) → D_4
  98. Polygon(A_4, B_4, C_4, D_4) → poly25, a_4, b_4, c_4, d_4
  99. Midpoint(G_4, F_4) → Center
  100. Segment(H_4, I_4) → f_4
  101. Segment(J_4, K_4) → g_4

AI Drawing Prompt Reference

Create an interactive geometric game demonstrating integer multiplication. Use randomly generated positive and negative integers as initial values. Construct multiple polygons through geometric transformations, where each polygon rotates around its center by specific angles and translates, forming a series of similar shapes in different positions. Finally, display the combined dynamic effect of multiple polygons for educational purposes.
The prompt above was compiled from the original drawing commands and is for reference only.