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Decimal Division 1.5/3 Demonstration

Decimal Division 1.5/3 Demonstration
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2019-03-14 18:23
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the decimal division calculation of 1.5 by 3, visualizing the process and result. Core math concepts include decimal division, rational number operations, and equation representation. GeoGebra commands/objects used in construction are Segment, Sequence, Point, Join, If, Element. Suitable for middle school mathematics teaching, helping students understand the geometric meaning and calculation method of decimal division.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, D) → g
  3. Segment(D, C) → h
  4. Segment(C, A) → i
  5. Segment(F, G) → j
  6. Segment(G, H) → k
  7. Segment(H, E) → l
  8. Segment(E, F) → m
  9. Segment(J, L) → n
  10. Segment(L, K) → p
  11. Segment(K, I) → q
  12. Segment(I, J) → r
  13. Sequence((k, 15), k, 8, 18) → l1
  14. Sequence((k, 25), k, 8, 18) → l2
  15. Sequence(Polygon[Element[l1, k], Element[l1, k + 1], Element[l2, k + 1], Element[l2, k]], k, 1, 10) → l3
  16. Sequence((k, 15), k, 20, 29) → l4
  17. Sequence((k, 25), k, 20, 29) → l5
  18. Sequence(Polygon[Element[l4, k], Element[l4, k + 1], Element[l5, k + 1], Element[l5, k]], k, 1, 10, 2) → l6
  19. Sequence((k, 0), k, 1, 9, 2) → l7
  20. Sequence((k, 0), k, 13, 21, 2) → l8
  21. Sequence((k, 0), k, 25, 33, 2) → l9
  22. Sequence(Element[l1, k], k, 1, 11, 3) → l10
  23. Point(l6) → M
  24. Join({l10, l11}) → l12
  25. Sequence(Vector[Element[l12, k], Element[l7, k]], k, 1, 5) → l13
  26. Sequence(Element[l1, k], k, 2, 10, 3) → l14
  27. Point(l6) → N
  28. Point(l6) → O
  29. Join({l14, l15}) → l16
  30. Sequence(Vector[Element[l16, k], Element[l8, k]], k, 1, 5) → l17
  31. Sequence(Element[l1, k], k, 3, 10, 3) → l18
  32. Point(l6) → P
  33. Point(l6) → Q
  34. Join({l18, l19}) → l20
  35. Sequence(Vector[Element[l20, k], Element[l9, k]], k, 1, 5) → l21
  36. If(0 ≤ a < 1, Vector[Dilate[Element[l13, 1], a]], Vector[If[a ≥ 1, Vector[Element[l13, 1]]]]) → u
  37. If(1 ≤ a < 2, Vector[Dilate[Element[l17, 1], a - 1]], Vector[If[a ≥ 2, Vector[Element[l17, 1]]]]) → v
  38. If(2 ≤ a < 3, Vector[Dilate[Element[l21, 1], a - 2]], Vector[If[a ≥ 3, Vector[Element[l21, 1]]]]) → w
  39. If(3 ≤ a < 4, Vector[Dilate[Element[l13, 2], a - 3]], Vector[If[a ≥ 4, Vector[Element[l13, 2]]]]) → b
  40. If(4 ≤ a < 5, Vector[Dilate[Element[l17, 2], a - 4]], Vector[If[a ≥ 5, Vector[Element[l17, 2]]]]) → c
  41. If(5 ≤ a < 6, Vector[Dilate[Element[l21, 2], a - 5]], Vector[If[a ≥ 6, Vector[Element[l21, 2]]]]) → d
  42. If(6 ≤ a < 7, Vector[Dilate[Element[l13, 3], a - 6]], Vector[If[a ≥ 7, Vector[Element[l13, 3]]]]) → e
  43. If(7 ≤ a < 8, Vector[Dilate[Element[l17, 3], a - 7]], Vector[If[a ≥ 8, Vector[Element[l17, 3]]]]) → s
  44. If(8 ≤ a < 9, Vector[Dilate[Element[l21, 3], a - 8]], Vector[If[a ≥ 9, Vector[Element[l21, 3]]]]) → t
  45. If(9 ≤ a < 10, Vector[Dilate[Element[l13, 4], a - 9]], Vector[If[a ≥ 10, Vector[Element[l13, 4]]]]) → u_1
  46. If(10 ≤ a < 11, Vector[Dilate[Element[l17, 4], a - 10]], Vector[If[a ≥ 11, Vector[Element[l17, 4]]]]) → v_1
  47. If(11 ≤ a < 12, Vector[Dilate[Element[l21, 4], a - 11]], Vector[If[a ≥ 12, Vector[Element[l21, 4]]]]) → w_1
  48. If(12 ≤ a < 13, Vector[Dilate[Element[l13, 5], a - 12]], Vector[If[a ≥ 13, Vector[Element[l13, 5]]]]) → a_1
  49. If(13 ≤ a < 14, Vector[Dilate[Element[l17, 5], a - 13]], Vector[If[a ≥ 14, Vector[Element[l17, 5]]]]) → b_1
  50. If(14 ≤ a < 15, Vector[Dilate[Element[l21, 5], a - 14]], Vector[If[a ≥ 15, Vector[Element[l21, 5]]]]) → c_1
  51. Join({l3, l6}) → l23
  52. Sequence(Translate[Element[l23, k], Vector[Element[l22, k]]], k, 1, 15) → l24
  53. Element(l3, 1) → q1
  54. Element(l3, 2) → q2
  55. Element(l3, 3) → q3
  56. Element(l3, 4) → q4
  57. Element(l3, 5) → q5
  58. Element(l3, 6) → q6
  59. Element(l3, 7) → q7
  60. Element(l3, 8) → q8
  61. Element(l3, 9) → q9
  62. Element(l3, 10) → q10
  63. Element(l6, 1) → q11
  64. Element(l6, 2) → q12
  65. Element(l6, 3) → q13
  66. Element(l6, 4) → q14
  67. Element(l6, 5) → q15

AI Drawing Prompt Reference

Create a visual representation demonstrating the decimal division of 1.5 by 3, highlighting core math concepts like decimal division, rational number operations, and equation representation. Start by drawing a square composed of four line segments. Inside the square, construct two sets of parallel quadrilaterals to represent the division of 1.5 and 3. Connect the vertices of these quadrilaterals and the square to form multiple triangles, using distinct colors or line styles. Finally, add dynamic vectors that scale or maintain their original length based on the input value 'a', showing the result of the division in three directions.
The prompt above was compiled from the original drawing commands and is for reference only.