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Fraction Strip Comparison: Exploring Fraction Size and Equivalence

Fraction Strip Comparison: Exploring Fraction Size and Equivalence
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2023-02-15 19:50
PolygonInequalityGeometric ConstructionSlider Animation
In collections Zahlenstrahl und Ordnen von Brüchen
This GeoGebra example uses an interactive 'fraction strip' (Streifentafel) to help students visually compare the sizes of fractions. The strip is divided into equal parts, and students can move an orange marker to locate a specific fraction, then observe the length of the corresponding segment to determine whether the fraction is smaller or larger than a reference value (e.g., 1/2). Core mathematical concepts include relative size of fractions, fractions as parts of a whole, equivalent fractions (e.g., 2/4 = 1/2), and strategies for comparing fractions. Construction highlights: the applet uses GeoGebra commands such as Polygon, Point, Line, Intersect, Segment, OrthogonalLine, and If to build the strip, division lines, markers, and dynamic feedback; objects include multiple points (e.g., A82, B82) and segments, with conditional logic for interactivity. Suitable for grades 5-6, this resource supports classroom exploration and practice, helping students develop number sense and reasoning about fraction comparison and equivalence.

GeoGebra Commands & Parameters

  1. Polygon(AA3, AA4, AA15, AA14) → VA3, h, a4, a15, i
  2. Point(yAxis) → B
  3. Line(B, xAxis) → n_5
  4. Point(n_5) → E
  5. Intersect(n_5, yAxis) → D
  6. Segment(D, E) → q_5
  7. Polygon(AA1, AA2, AA13, AA12) → VA1, a1, a2, a13, a12
  8. Polygon(AA2, AA3, AA14, AA13) → VA2, f, a3, a14, g
  9. Polygon(AA4, AA5, AA16, AA15) → VA4, j, a5, a16, k
  10. Polygon(AA5, AA6, AA17, AA16) → VA5, l, a6, a17, m
  11. Polygon(AA6, AA7, AA18, AA17) → VA6, n, a7, a18, p
  12. Polygon(AA7, AA8, AA19, AA18) → VA7, q, a8, a19, r
  13. Polygon(AA8, AA9, AA20, AA19) → VA8, s, a9, a20, t
  14. Polygon(AA9, AA10, AA21, AA20) → VA9, a23, a10, a21, c
  15. Polygon(AA10, AA11, AA22, AA21) → VA10, d, a11, a22, e
  16. Polygon(AC1, AC2, AC12, AC11) → VC1, a_1, b_1, l_1, k_1
  17. Polygon(AC2, AC3, AC13, AC12) → VC2, b_2, c_1, m_1, l_2
  18. Polygon(AC3, AC4, AC14, AC13) → VC3, c_2, d_1, n_1, m_2
  19. Polygon(AC4, AC5, AC15, AC14) → VC4, d_2, e_1, o, n_2
  20. Polygon(AC5, AC6, AC16, AC15) → VC5, e_2, f_1, p_1, o_1
  21. Polygon(AC6, AC7, AC17, AC16) → VC6, f_2, g_1, q_1, p_2
  22. Polygon(AC7, AC8, AC18, AC17) → VC7, g_2, h_1, r_1, q_2
  23. Polygon(AC8, AC9, AC19, AC18) → VC8, h_2, i_1, a24, r_2
  24. Polygon(AC9, AC10, AC20, AC19) → VC9, i_2, j_1, t_1, s_2
  25. Polygon(AE1, AE2, AE11, AE10) → VE1, e1, e2, e11, e10
  26. Polygon(AE2, AE3, AE12, AE11) → VE2, s_1, e3, e12, j_2
  27. Polygon(AE3, AE4, AE13, AE12) → VE3, k_2, e4, e13, t_2
  28. Polygon(AE4, AE5, AE14, AE13) → VE4, a_2, e5, e14, f_3
  29. Polygon(AE5, AE6, AE15, AE14) → VE5, g_3, e6, e15, h_3
  30. Polygon(AE6, AE7, AE16, AE15) → VE6, i_3, e7, e16, j_3
  31. Polygon(AE7, AE8, AE17, AE16) → VE7, k_3, e8, e17, l_3
  32. Polygon(AE8, AE9, AE18, AE17) → VE8, m_3, e9, e18, n_3
  33. Polygon(AG1, AG2, AG10, AG9) → VG1, g1, g2, g10, g9
  34. Polygon(AG2, AG3, AG11, AG10) → VG2, p_3, g3, g11, q_3
  35. Polygon(AG3, AG4, AG12, AG11) → VG3, r_3, g4, g12, s_3
  36. Polygon(AG4, AG5, AG13, AG12) → VG4, t_3, g5, g13, a_3
  37. Polygon(AG5, AG6, AG14, AG13) → VG5, b_3, g6, g14, c_3
  38. Polygon(AG6, AG7, AG15, AG14) → VG6, d_3, g7, g15, e_3
  39. Polygon(AG7, AG8, AG16, AG15) → VG7, f_4, g8, g16, g_4
  40. Polygon(AI1, AI2, AI9, AI8) → VI1, i1, i2, i9, i8
  41. Polygon(AI2, AI3, AI10, AI9) → VI2, h_4, i3, i10, i_4
  42. Polygon(AI3, AI4, AI11, AI10) → VI3, j_4, i4, i11, k_4
  43. Polygon(AI4, AI5, AI12, AI11) → VI4, l_4, i5, i12, m_4
  44. Polygon(AI5, AI6, AI13, AI12) → VI5, n_4, i6, i13, p_4
  45. Polygon(AI6, AI7, AI14, AI13) → VI6, q_4, i7, i14, r_4
  46. Polygon(AK1, AK2, AK8, AK7) → VK1, k1, k2, k8, k7
  47. Polygon(AK2, AK3, AK9, AK8) → VK2, s_4, k3, k9, t_4
  48. Polygon(AK3, AK4, AK10, AK9) → VK3, a_4, k4, k10, b_4
  49. Polygon(AK4, AK5, AK11, AK10) → VK4, c_4, k5, k11, d_4
  50. Polygon(AK5, AK6, AK12, AK11) → VK5, e_4, k6, k12, f_5
  51. Polygon(AM1, AM2, AM7, AM6) → VM1, m1, m2, m7, m6
  52. Polygon(AM2, AM3, AM8, AM7) → VM2, g_5, m3, m8, h_5
  53. Polygon(AM3, AM4, AM9, AM8) → VM3, i_5, m4, m9, j_5
  54. Polygon(AM4, AM5, AM10, AM9) → VM4, k_5, m5, m10, l_5
  55. Polygon(AO1, AO2, AO6, AO5) → VO1, a_5, b_5, f_6, e_5
  56. Polygon(AO2, AO3, AO7, AO6) → VO2, b_6, c_5, g_6, f_7
  57. Polygon(AO3, AO4, AO8, AO7) → VO3, c_6, d_5, h_6, g_7
  58. Polygon(AQ1, AQ2, AQ5, AQ4) → VQ1, a_6, b_7, e_6, d_6
  59. Polygon(AQ2, AQ3, AQ6, AQ5) → VQ2, b_8, c_7, f_8, e_7
  60. Polygon(AS1, AS2, AS4, AS3) → VS1, a_7, b_9, d_7, c_8
  61. Point(Alle) → A
  62. OrthogonalLine(A, xAxis) → m_5
  63. Intersect(m_5, xAxis) → C
  64. If(Lineal ≟ A3, true) → ZweiZehntel
  65. If(Lineal ≟ E3, true) → ZweiAchtel
  66. If(Lineal ≟ I3, true) → ZweiSechstel
  67. If(Lineal ≟ A5, true) → VierZehntel
  68. If(Lineal ≟ A6, true) → FünfZehntel
  69. If(Lineal ≟ A7, true) → SechsZehntel
  70. If(Lineal ≟ I5, true) → VierSechstel
  71. If(Lineal ≟ E7, true) → SechsAchtel
  72. If(Lineal ≟ A9, true) → AchtZehntel
  73. If(Lineal ≟ S2, true) → Ganzes
  74. Polygon(B_8, C_8, D_8, E_8) → v1, r_5, s_5, d_8, e_8
  75. Segment(A, C_{42}) → p_5

AI Drawing Prompt Reference

Draw a fraction strip graphic: divide a long line segment into equal parts, and place a movable orange marker line on it. Students can move the marker to observe the length of the corresponding segment and compare it with a reference value (e.g., 1/2). The graphic should include the concept of equivalent fractions, such as 2/4 and 1/2 representing the same length. Construct by first drawing the long strip, then adding equal division lines and the marker line, and finally adding a reference line for comparison.
The prompt above was compiled from the original drawing commands and is for reference only.