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Multiple Models for Proper Fractions by hoganl

Multiple Models for Proper Fractions by hoganl
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2013-11-05 00:56
Coordinate GeometryGeometric ConstructionGraphing
In collections fifth grade fractions
This example demonstrates how to display and compare proper fractions using various models including linear, number line, set, and area representations. Key math concepts involve fraction representation, number line, set theory, and area models. Construction highlights the use of GeoGebra commands like Segment, Point, Circle, Sequence, Max, Min, If, Polygon, Vector, Rotate, CircleSector along with objects such as num, denom, etc. Suitable for elementary and higher mathematics education to visually understand different representations of proper fractions.

GeoGebra Commands & Parameters

  1. Segment(K_2, K_2 + (1 - num / denom, 0)) → linearModel1SegShift
  2. Point(linearModel1SegShift) → LinearModel1PtL
  3. Circle(R_1, T_1) → Circle_{model}
  4. Point(Circle[R_1, 0.105]) → C_2
  5. Sequence(If[round(flex * x(Element[list1, i]) / y(Element[list1, i])) / flex ≟ round(flex * x(L_1)) / flex, i, 0], i, 1, Length[list1]) → list2
  6. Max(list2) → match
  7. Min(9 / denom, 1) → a9
  8. Min(4 / denom, 1) → a4
  9. Min(5 / denom, 1) → a5
  10. Min(8 / denom, 1) → a8
  11. Min(7 / denom, 1) → a7
  12. Min(6 / denom, 1) → a6
  13. Min(1 / denom, 1) → a1
  14. Min(2 / denom, 1) → a2
  15. If(denom < 10, " " + denom, "" + denom) → formatd
  16. Min(3 / denom, 1) → a3
  17. Min(10 / denom, 1) → a10
  18. Point(Circle[M, 1]) → Q
  19. Point(Circle[N, 1]) → R
  20. Point(Circle[L_1, 0.02]) → U_1
  21. Point(Circle[U_1, 0.5]) → V_1
  22. Polygon(LinearModel1PtL + (0, -0.03), LinearModel1PtL + (num / denom, -0.03), LinearModel1PtL + (num / denom, 0.03), LinearModel1PtL + (0, 0.03)) → int1, a, b, c, e
  23. If(impr > 1, 1, 0) → Rect_{show}
  24. Vector(NL_c, NL_l) → u
  25. Vector(NL_c, NL_r) → v
  26. Vector(FP_t, FP) → w
  27. If(num / denom > 1, 1, 0) → Set_{show}
  28. Segment((1, 0.13), (1, 0.17)) → i_2
  29. Segment((0, 0.13), (0, 0.17)) → j_2
  30. Segment(R_1, C_2) → m_2
  31. Rotate(C_2, angle, R_1) → D_2
  32. CircleSector(R_1, C_2, D_2) → r_3
  33. Segment(R_1, D_2) → l_2
  34. Rotate(C_2, (360 / denom)°, R_1) → B_2
  35. Sequence(Segment[Rotate[C_2, (360 * i / denom)°, R_1], R_1], i, 0, denom) → Angle_{divseq}
  36. Segment(K_2, L_2) → a_2
  37. Vector((0, 0.25), (0.1, 0.25)) → image_{vector}
  38. Sequence(Translate[pic1, Vector[i * image_{vector}]], i, 0, denom - 1) → Set_{opencat}
  39. Sequence(Translate[pic2, Vector[i * image_{vector}]], i, 0, num - 1) → Set_{closedcat}
  40. Sequence(Translate[pic3, Vector[i * image_{vector}]], i, 0, denom - 1) → Set_{openstar}
  41. Sequence(Translate[pic4, Vector[i * image_{vector}]], i, 0, num - 1) → Set_{closedstar}
  42. Sequence(Segment[(0.045 + i / 11, 0.385), Point[Circle[(0.045 + i / 11, 0.59), 0]]], i, 0, denom) → Area_{rectdiv}
  43. Polygon(R_8, F_2, G_2, E_2) → rect_{red}, r_8, f_4, g_4, e_4
  44. Segment(R_8, I_2) → b_2
  45. Segment(E_2, H_2) → n_2
  46. Sequence(Segment[(0.045 + i / (3 * denom), 0.385), Point[Circle[(0.045 + i / (3 * denom), 0.59), 0]]], i, 0, denom) → Area_{rect2}
  47. Segment(E_2, M_2) → a_3
  48. Segment(J_2, R_8) → b_3
  49. Polygon(E_2, O_2, N_2, R_8) → poly1, e_5, o_2, n_3, r_4
  50. Segment(LinearModel1PtL + (0, 0.0050), LinearModel1PtR + (0, 0.0050)) → linearModel1Line
  51. Sequence(Segment[(i, 0.13), (i, 0.17)], i, 0, 1, 1 / lineHashMarks) → lineHashMarkList
  52. Sequence(Segment[(i, 0), (i, 0.05)], i, 0, 1, 1 / lineHashMarks) → linearHashMarkList
  53. Sequence(Circle[(0.05 + i, 0.3), 0.045], i, 0, (denom - 1) / 10, 0.1) → setCircleOpen
  54. Sequence(Circle[(0.05 + i, 0.3), 0.04], i, 0, (num - 1) / 10, 0.1) → setCircleShading