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Grid Multiplication

Grid Multiplication
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2015-02-07 20:10
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example dynamically demonstrates grid multiplication to visually illustrate the geometric meaning of multiplication. It involves core math concepts like multiplication, equations, frequency distribution, and statistical characteristics. Construction highlights the use of Polygon, Segment, PointIn, OrthogonalLine, Intersect, Distance, and Midpoint commands in GeoGebra. Suitable for middle school and above, helping learners understand the connection between multiplication and geometric shapes, enhancing spatial reasoning.

GeoGebra Commands & Parameters

  1. Polygon(Ay, ABxy, Bx, A) → poly5, ay_1, abxy_1, bx_1, a_2
  2. Segment(Ay, ABxy) → c
  3. Segment(ABxy, Bx) → d
  4. Segment(Bx, A) → e
  5. Segment(Ay, A) → f
  6. PointIn(poly5) → B
  7. OrthogonalLine(B, xAxis) → g
  8. OrthogonalLine(B, yAxis) → h
  9. Intersect(g, c) → C
  10. Intersect(h, d) → F
  11. Intersect(h, f) → D
  12. Intersect(g, e) → E
  13. Segment(D, B) → i
  14. Segment(B, F) → j
  15. Segment(C, B) → k
  16. Segment(B, E) → l
  17. Polygon(Ay, C, B, D) → poly1, ay, c_1, b_1, d_1
  18. Polygon(C, ABxy, F, B) → poly2, c_2, abxy, f_1, b_2
  19. Polygon(B, F, Bx, E) → poly3, b_3, f_2, bx, e_1
  20. Polygon(D, B, E, A) → poly4, d_2, b_4, e_2, a_1
  21. Intersect(i, k) → G
  22. Distance(C, Ay) → dAyC
  23. Midpoint(Ay, C) → H
  24. Midpoint(C, B) → I
  25. Midpoint(C, ABxy) → J
  26. Midpoint(B, E) → K
  27. Midpoint(B, F) → L
  28. Midpoint(B, D) → M
  29. Midpoint(A, E) → N
  30. Midpoint(E, Bx) → O
  31. Midpoint(Bx, F) → P
  32. Midpoint(D, A) → Q
  33. Midpoint(Ay, D) → R
  34. Midpoint(R, I) → S
  35. Midpoint(ABxy, F) → T
  36. Midpoint(I, T) → U
  37. Midpoint(K, P) → V
  38. Midpoint(Q, K) → W
  39. Midpoint(ABxy, Bx) → Z
  40. Midpoint(Ay, ABxy) → A_1
  41. Distance(ABxy, C) → dCABxy
  42. Distance(ABxy, Ay) → dABxyAy
  43. Distance(ABxy, F) → dABxyF
  44. Distance(F, Bx) → dFBx
  45. Distance(ABxy, Bx) → dABxyBx
  46. Distance(C, B) → dCB
  47. Distance(B, E) → dBE
  48. Distance(F, B) → dFB
  49. Distance(B, D) → dBD