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Betty's Quincenañera: Two Representations of a Ratio – Strip Diagram and Double

Betty's Quincenañera: Two Representations of a Ratio – Strip Diagram and Double
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2019-05-23 04:46
PolygonTransformationGeometric ConstructionGraphing
This GeoGebra example, titled 'Betty's Quincenañera', demonstrates how to represent a single ratio using two complementary visual models: a strip diagram and a double number line. The core mathematical concept is the equivalence of ratio representations, showing how a real-world context (such as quantities for a birthday celebration) can be translated into proportional lengths and aligned number scales. The construction uses a variety of GeoGebra commands including Point, Segment, Line, OrthogonalLine, Intersect, Polygon, Midpoint, Vector, Translate, Distance, and Circle to build the geometric framework. Key objects include multiple points, segments, polygons, and auxiliary lines that structure the proportional divisions. This resource is ideal for middle school students learning ratios, proportions, and percentages, as well as for teachers seeking to illustrate multiple visual strategies for the same mathematical relationship. It fosters a deeper understanding of how different diagrams can convey identical proportional information, enhancing flexibility in problem-solving.

GeoGebra Commands & Parameters

  1. Point(Circle[A, a]) → B
  2. Segment(A, B) → f
  3. Line(C, f) → g
  4. OrthogonalLine(A, g) → h
  5. OrthogonalLine(B, g) → i
  6. Intersect(g, h) → D
  7. Intersect(g, i) → E
  8. Polygon(A, D, E, B) → poly1, a_1, d, e, b
  9. Point(Circle[B, b]) → F
  10. Segment(B, F) → j
  11. Point(Circle[F, b]) → G
  12. Segment(F, G) → k
  13. Point(Circle[G, b]) → H
  14. Segment(G, H) → l
  15. Point(Circle[H, b]) → I
  16. Segment(H, I) → m
  17. Point(Circle[I, b]) → J
  18. Segment(I, J) → n
  19. Point(Circle[J, b]) → K
  20. Segment(J, K) → p
  21. OrthogonalLine(F, g) → q
  22. OrthogonalLine(G, g) → r
  23. OrthogonalLine(H, g) → s
  24. OrthogonalLine(I, g) → t
  25. OrthogonalLine(J, g) → c
  26. OrthogonalLine(K, g) → f_1
  27. Intersect(g, q) → L
  28. Intersect(g, r) → M
  29. Intersect(g, s) → N
  30. Intersect(g, t) → O
  31. Intersect(g, c) → P
  32. Intersect(g, f_1) → Q
  33. Polygon(B, F, L, E) → poly2, b_1, f_2, l_1, e_1
  34. Polygon(F, G, M, L) → poly3, f_3, g_1, m_1, l_2
  35. Polygon(G, H, N, M) → poly4, g_2, h_1, n_1, m_2
  36. Polygon(H, I, O, N) → poly5, h_2, i_1, o, n_2
  37. Polygon(I, J, P, O) → poly6, i_2, j_1, p_1, o_1
  38. Polygon(J, K, Q, P) → poly7, j_2, k_1, q_1, p_2
  39. Intersect(g, h) → R
  40. Line(A, R) → r_1
  41. Point(r_1) → S
  42. OrthogonalLine(S, r_1) → s_1
  43. Intersect(r, s_1) → T
  44. Segment(S, T) → t_1
  45. Intersect(f_1, s_1) → U
  46. Segment(T, U) → c_1
  47. Midpoint(S, T) → V
  48. Midpoint(T, U) → W
  49. Point(r_1) → Z
  50. Point(r_1) → A_1
  51. Segment(Z, A_1) → d_1
  52. Point(d_1) → B_1
  53. Point(d_1) → C_1
  54. OrthogonalLine(B_1, d_1) → k_2
  55. OrthogonalLine(C_1, d_1) → q_2
  56. Point(k_2) → D_1
  57. Vector(B_1, D_1) → u
  58. Point(q_2) → E_1
  59. Vector(C_1, E_1) → v
  60. Point(u) → F_1
  61. OrthogonalLine(F_1, u) → r_2
  62. Point(v) → G_1
  63. Point(d_1) → H_1
  64. Vector(H_1, F_1) → w
  65. Translate(F_1, w) → I_1
  66. Translate(I_1, w) → J_1
  67. Translate(J_1, w) → K_1
  68. Translate(K_1, w) → L_1
  69. Translate(L_1, w) → M_1
  70. Translate(G_1, w) → N_1
  71. Translate(N_1, w) → O_1
  72. Translate(O_1, w) → P_1
  73. Translate(P_1, w) → Q_1
  74. Translate(Q_1, w) → R_1
  75. Midpoint(d_1) → U_1
  76. OrthogonalLine(U_1, d_1) → t_2
  77. Point(Circle[U_1, ((a * 3) * 40.36 / 18)]) → V_1
  78. Segment(U_1, V_1) → a_2
  79. Point(d_1) → S_1
  80. Distance(S_1, R_1) → distanceS1R1
  81. Point(Circle[U_1, ((distanceS1R1 / 18 * 3) * a)]) → T_1
  82. Segment(U_1, T_1) → s_2
  83. OrthogonalLine(T_1, t_2) → b_2
  84. Circle(T_1, 4) → c_2
  85. Intersect(c_2, b_2, 2) → W_1
  86. Intersect(c_2, b_2, 1) → Z_1
  87. Segment(W_1, Z_1) → d_2

AI Drawing Prompt Reference

Draw a horizontal rectangle as a strip diagram, divided into seven equal vertical sections by equally spaced perpendicular lines from the base. Above the rectangle, construct a parallel line starting from the left endpoint, marking seven equally spaced points along it with the same unit length, and draw perpendiculars through these points to form a double number line. Then, add a slanted auxiliary line from the rectangle's left side, place a point on it, drop a perpendicular to the base, and connect the intersection points to form a small triangle, illustrating an alternative ratio representation.
The prompt above was compiled from the original drawing commands and is for reference only.