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Multiplication Visualization Tool

Multiplication Visualization Tool
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2015-08-26 05:49
FunctionCoordinate GeometryGeometric Construction
This is a multiplication visualization tool that helps users understand multiplication operations intuitively. Core math concepts include functions and geometric construction. Commands used include Intersect, Line, OrthogonalLine, Polygon, and Segment. Suitable for high-grade elementary and junior high school students to learn multiplication and geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → origin
  2. Line(origin, xAxis) → y_0
  3. Line(origin, yAxis) → yaxis
  4. OrthogonalLine(xfactor1, y_0) → factor1line
  5. OrthogonalLine(yfactor2, yaxis) → factor2line
  6. Intersect(factor1line, factor2line) → xyfactors
  7. Polygon(origin, xfactor1, xyfactors, yfactor2) → poly1, origin_1, xfactor1_1, xyfactors_1, yfactor2_1
  8. Intersect(yaxis, y_{12}) → A
  9. Intersect(yaxis, y_{11}) → B
  10. Intersect(yaxis, y_{10}) → C
  11. Intersect(yaxis, y_9) → D
  12. Intersect(yaxis, y_8) → E
  13. Intersect(yaxis, y_7) → F
  14. Intersect(yaxis, y_6) → G
  15. Intersect(yaxis, y_5) → H
  16. Intersect(yaxis, y_4) → I
  17. Intersect(yaxis, y_3) → J
  18. Intersect(yaxis, y_2) → K
  19. Intersect(yaxis, y_1) → L
  20. Intersect(y_{12}, x_{12}) → M
  21. Intersect(y_{11}, x_{12}) → N
  22. Intersect(y_{10}, x_{12}) → O
  23. Intersect(y_9, x_{12}) → P
  24. Intersect(y_8, x_{12}) → Q
  25. Intersect(y_7, x_{12}) → R
  26. Intersect(y_6, x_{12}) → S
  27. Intersect(y_5, x_{12}) → T
  28. Intersect(y_4, x_{12}) → U
  29. Intersect(factor2line, y_3) → V
  30. Intersect(factor2line, y_3) → W
  31. Intersect(factor2line, y_3) → Z
  32. Intersect(y_2, x_{12}) → A_1
  33. Intersect(y_1, x_{12}) → B_1
  34. Intersect(y_3, x_{12}) → C_1
  35. Intersect(y_{12}, x_1) → D_1
  36. Intersect(y_{12}, x_2) → E_1
  37. Intersect(factor1line, y_{12}) → F_1
  38. Intersect(y_{12}, x_4) → G_1
  39. Intersect(y_{12}, x_5) → H_1
  40. Intersect(y_{12}, x_6) → I_1
  41. Intersect(y_{12}, x_7) → J_1
  42. Intersect(y_{12}, x_8) → K_1
  43. Intersect(y_{12}, x_9) → L_1
  44. Intersect(y_{12}, x_{10}) → M_1
  45. Intersect(y_{12}, x_{11}) → N_1
  46. Intersect(y_0, x_{12}) → O_1
  47. Intersect(y_0, x_{11}) → P_1
  48. Intersect(y_0, x_{10}) → Q_1
  49. Intersect(y_0, x_9) → R_1
  50. Intersect(y_0, x_8) → S_1
  51. Intersect(y_0, x_7) → T_1
  52. Intersect(y_0, x_6) → U_1
  53. Intersect(y_0, x_5) → V_1
  54. Intersect(y_0, x_4) → W_1
  55. Intersect(y_0, x_3) → Z_1
  56. Intersect(y_0, x_2) → A_2
  57. Intersect(y_0, x_1) → B_2
  58. Intersect(y_{12}, x_3) → C_2
  59. Intersect(factor2line, yaxis) → D_2
  60. Segment(A, M) → a
  61. Segment(B, N) → b
  62. Segment(C, O) → c
  63. Segment(D, P) → d
  64. Segment(E, Q) → e
  65. Segment(F, R) → f
  66. Segment(G, S) → g
  67. Segment(H, T) → h
  68. Segment(J, C_1) → j
  69. Segment(K, A_1) → k
  70. Segment(L, B_1) → l
  71. Segment(origin, O_1) → m
  72. Segment(A, origin) → n
  73. Segment(D_1, B_2) → p
  74. Segment(E_1, A_2) → q
  75. Segment(C_2, Z_1) → r
  76. Segment(F_1, xfactor1) → s
  77. Segment(H_1, V_1) → t
  78. Segment(I_1, U_1) → a_1
  79. Segment(J_1, T_1) → b_1
  80. Segment(K_1, S_1) → c_1
  81. Segment(L_1, R_1) → d_1
  82. Segment(M_1, Q_1) → e_1
  83. Segment(N_1, P_1) → f_1
  84. Segment(M, O_1) → g_1
  85. Segment(G_1, W_1) → h_1
  86. Segment(I, U) → i
  87. Polygon(origin, A, M, O_1) → poly2, origin_2, a_2, m_1, o_1

AI Drawing Prompt Reference

On a coordinate plane, start at the origin and draw two perpendicular lines along the horizontal and vertical axes. Pick a point on the horizontal axis and draw a vertical line through it; pick another point on the vertical axis and draw a horizontal line through it; these two lines intersect at a point. Connect the origin, the point on the horizontal axis, the intersection point, and the point on the vertical axis to form a rectangle. Then, mark equally spaced points along the vertical axis from the origin upward, and through each draw a horizontal line; similarly, mark equally spaced points along the horizontal axis from the origin rightward, and through each draw a vertical line. These parallel lines cross each other, forming a grid, and also intersect the axes and the rectangle sides, producing many intersection points that illustrate the correspondence of factors in multiplication.
The prompt above was compiled from the original drawing commands and is for reference only.