MathPlotAI Logo MathPlotAI

Multiplication Array with Three Dividers

Multiplication Array with Three Dividers
Loading the math board and drawing, please wait…
2015-01-14 06:55
PolygonFunctionSequenceGeometric ConstructionGraphing
This GeoGebra example demonstrates a visual array model for two-digit by two-digit multiplication, using a rectangle divided into multiple sub-rectangles to illustrate the distributive property of multiplication. The core mathematical concepts include integer multiplication, area models, and the distributive law (e.g., (a+b)×(c+d) expansion). The construction uses GeoGebra commands such as Intersect, Point, Segment, Line, Ray, Polygon, and Distance to create a grid of points (A, B, C, D, etc.) and segments (a, b, c, etc.), with three dividers splitting the large rectangle into smaller regions, each representing a partial product. This resource is suitable for upper elementary or middle school students to grasp the geometric meaning of multi-digit multiplication, and for teachers to use in classroom demonstrations connecting abstract arithmetic with visual area representations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Segment(A, B) → a
  4. Point(yAxis) → C
  5. Segment(A, C) → b
  6. Point(b) → D
  7. Segment(A, D) → c
  8. Line(D, a) → d
  9. Line(B, c) → e
  10. Intersect(d, e) → E
  11. Segment(D, E) → f
  12. Segment(E, B) → g
  13. Point(a) → F
  14. Line(F, c) → h
  15. Ray(A, B) → i
  16. Point(i) → G
  17. Segment(B, G) → j
  18. Line(G, g) → k
  19. Intersect(d, h) → H
  20. Polygon(H, F, B, E) → poly1, h_1, f_1, b_1, e_1
  21. Point(j) → I
  22. Line(I, g) → l
  23. Intersect(d, l) → J
  24. Polygon(B, I, J, E) → poly2, b_2, i_1, j_1, e_2
  25. Intersect(d, k) → K
  26. Polygon(I, G, K, J) → poly3, i_2, g_1, k_1, j_2
  27. Polygon(A, F, H, D) → poly4, a_1, f_2, h_2, d_1
  28. Segment(D, A) → m
  29. Segment(G, A) → n
  30. Segment(G, K) → p
  31. Segment(K, D) → q
  32. Segment(H, F) → r
  33. Segment(E, B) → s
  34. Segment(J, I) → t
  35. Distance(A, D) → distanceAD
  36. Distance(D, H) → distanceDH
  37. Distance(H, E) → distanceHE
  38. Distance(E, J) → distanceEJ
  39. Distance(J, K) → distanceJK

AI Drawing Prompt Reference

Draw a large rectangle with its lower-left corner at the origin, its horizontal side along the x-axis, and its vertical side along the y-axis. Place two points on the horizontal side and one point on the vertical side, then draw lines through these points parallel to the opposite axes, dividing the rectangle into four smaller rectangles. Extend the horizontal side to the right and place an additional point, from which draw a line parallel to an internal vertical line, further subdividing the right region. The result is a grid of smaller rectangles, each representing a partial product in the distributive property of multiplication. Mark the distances between the division points along the sides and highlight the boundaries of each sub-rectangle.
The prompt above was compiled from the original drawing commands and is for reference only.