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Comparing Rational Numbers – Fractions

Comparing Rational Numbers – Fractions
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2020-08-18 22:15
InequalityGeometric ConstructionGraphing
This GeoGebra example demonstrates a visual approach to comparing rational numbers and fractions, allowing students to observe their relative positions on a number line and understand inequality relationships. Key mathematical concepts include rational numbers, fraction comparison, inequalities, and number line representation. In terms of construction, it employs Min and Max commands to set ranges, If commands for conditional logic, Segment and Polygon to draw geometric elements like number lines and fraction bars, Text for labels, and Point to define key locations. Objects such as NumLnFrac1 and NumLnFrac2 represent the positions of fractions, while factor variables enable adjustments. The example is suitable for middle school math education, particularly for teaching fraction comparison through interactive visualization.

GeoGebra Commands & Parameters

  1. Min(c_1, d) → c
  2. Max(Sequence[If[Mod[c, i] + Mod[d, i] ≟ 0, i, -1], i, 1, Min[{c, d}]]) → factor_2
  3. If(factor_2 > 0, factor_2, 1) → factor_4
  4. Min(a_1, b) → a
  5. Max(Sequence[If[Mod[a, i] + Mod[b, i] ≟ 0, i, -1], i, 1, Min[{a, b}]]) → factor_1
  6. If(factor_1 > 0, factor_1, b) → factor_3
  7. Max(Sequence[If[Mod[l, i] + Mod[n, i] ≟ 0, i, -1], i, 1, Min[{l, n}]]) → factor
  8. Segment(C, D) → e
  9. Segment((x(C) + (1 / 8 * (x(D) - x(C))), y(C) + 0.1), (x(C) + (1 / 8 * (x(D) - x(C))), y(C) - 0.1)) → g
  10. Segment((x(C) + (0 / 8 * (x(D) - x(C))), y(C) + 0.2), (x(C) + (0 / 8 * (x(D) - x(C))), y(C) - 0.2)) → f
  11. Segment((x(C) + (2 / 8 * (x(D) - x(C))), y(C) + 0.2), (x(C) + (2 / 8 * (x(D) - x(C))), y(C) - 0.2)) → h
  12. Segment((x(C) + (3 / 8 * (x(D) - x(C))), y(C) + 0.1), (x(C) + (3 / 8 * (x(D) - x(C))), y(C) - 0.1)) → i
  13. Segment((x(C) + (4 / 8 * (x(D) - x(C))), y(C) + 0.2), (x(C) + (4 / 8 * (x(D) - x(C))), y(C) - 0.2)) → j
  14. Segment((x(C) + (5 / 8 * (x(D) - x(C))), y(C) + 0.1), (x(C) + (5 / 8 * (x(D) - x(C))), y(C) - 0.1)) → p
  15. Segment((x(C) + (6 / 8 * (x(D) - x(C))), y(C) + 0.2), (x(C) + (6 / 8 * (x(D) - x(C))), y(C) - 0.2)) → q
  16. Segment((x(C) + (7 / 8 * (x(D) - x(C))), y(C) + 0.1), (x(C) + (7 / 8 * (x(D) - x(C))), y(C) - 0.1)) → r
  17. Segment((x(C) + (8 / 8 * (x(D) - x(C))), y(C) + 0.2), (x(C) + (8 / 8 * (x(D) - x(C))), y(C) - 0.2)) → s
  18. Polygon(G, H, I, J) → poly1, g_1, h_1, i_1, j_1
  19. Segment(H, I) → t
  20. Segment(G, H) → b_1
  21. Segment(I, J) → d_1
  22. Segment(J, G) → e_1
  23. Polygon(G, (x(G) + (a / b * (x(H) - x(G))), y(G)), (x(J) + (a / b * (x(H) - x(G))), y(J)), J) → poly2, g_2, f_1, k_1, j_2
  24. Segment((x(G) + (1 / b * (x(H) - x(G))), y(G)), (x(G) + (1 / b * (x(H) - x(G))), y(G) - 1)) → l_1
  25. Segment((x(G) + (2 / b * (x(H) - x(G))), y(G)), (x(G) + (2 / b * (x(H) - x(G))), y(G) - 1)) → m_1
  26. Segment((x(G) + (3 / b * (x(H) - x(G))), y(G)), (x(G) + (3 / b * (x(H) - x(G))), y(G) - 1)) → n_1
  27. Segment((x(G) + (4 / b * (x(H) - x(G))), y(G)), (x(G) + (4 / b * (x(H) - x(G))), y(G) - 1)) → p_1
  28. Segment((x(G) + (5 / b * (x(H) - x(G))), y(G)), (x(G) + (5 / b * (x(H) - x(G))), y(G) - 1)) → q_1
  29. Segment((x(G) + (6 / b * (x(H) - x(G))), y(G)), (x(G) + (6 / b * (x(H) - x(G))), y(G) - 1)) → r_1
  30. Segment((x(G) + (7 / b * (x(H) - x(G))), y(G)), (x(G) + (7 / b * (x(H) - x(G))), y(G) - 1)) → s_1
  31. Segment((x(G) + (8 / b * (x(H) - x(G))), y(G)), (x(G) + (8 / b * (x(H) - x(G))), y(G) - 1)) → t_1
  32. Segment((x(G) + (9 / b * (x(H) - x(G))), y(G)), (x(G) + (9 / b * (x(H) - x(G))), y(G) - 1)) → a_2
  33. Segment((x(G) + (10 / b * (x(H) - x(G))), y(G)), (x(G) + (10 / b * (x(H) - x(G))), y(G) - 1)) → b_2
  34. Segment((x(G) + (11 / b * (x(H) - x(G))), y(G)), (x(G) + (11 / b * (x(H) - x(G))), y(G) - 1)) → c_2
  35. Polygon(K, L, M, N) → poly3, k_2, l_2, m_2, n_2
  36. Polygon(K, (x(K) + (c / d * (x(L) - x(K))), y(K)), (x(K) + (c / d * (x(L) - x(K))), y(M)), N) → poly4, k_3, d_2, e_2, n_3
  37. Segment((x(K) + (1 / d * (x(L) - x(K))), y(K)), (x(K) + (1 / d * (x(L) - x(K))), y(K) - 1)) → f_2
  38. Segment((x(K) + (2 / d * (x(L) - x(K))), y(K)), (x(K) + (2 / d * (x(L) - x(K))), y(K) - 1)) → h_2
  39. Segment((x(K) + (3 / d * (x(L) - x(K))), y(K)), (x(K) + (3 / d * (x(L) - x(K))), y(K) - 1)) → i_2
  40. Segment((x(K) + (4 / d * (x(L) - x(K))), y(K)), (x(K) + (4 / d * (x(L) - x(K))), y(K) - 1)) → p_2
  41. Segment((x(K) + (5 / d * (x(L) - x(K))), y(K)), (x(K) + (5 / d * (x(L) - x(K))), y(K) - 1)) → q_2
  42. Segment((x(K) + (6 / d * (x(L) - x(K))), y(K)), (x(K) + (6 / d * (x(L) - x(K))), y(K) - 1)) → r_2
  43. Segment((x(K) + (7 / d * (x(L) - x(K))), y(K)), (x(K) + (7 / d * (x(L) - x(K))), y(K) - 1)) → s_2
  44. Segment((x(K) + (8 / d * (x(L) - x(K))), y(K)), (x(K) + (8 / d * (x(L) - x(K))), y(K) - 1)) → t_2
  45. Segment((x(K) + (9 / d * (x(L) - x(K))), y(K)), (x(K) + (9 / d * (x(L) - x(K))), y(K) - 1)) → a_3
  46. Segment((x(K) + (10 / d * (x(L) - x(K))), y(K)), (x(K) + (10 / d * (x(L) - x(K))), y(K) - 1)) → b_3
  47. Segment((x(K) + (11 / d * (x(L) - x(K))), y(K)), (x(K) + (11 / d * (x(L) - x(K))), y(K) - 1)) → c_3
  48. Polygon(BoxPt, BoxPt + (9, 0), BoxPt + (9, If[ans ∧ words, -4, -3]), BoxPt + (0, If[ans ∧ words, -4, -3])) → box, d_3, e_3, f_3, g_3
  49. If(c > 9 ∨ d > 9, "_______", "____") → frac2Vinculum
  50. If(a > 9 ∨ b > 9, "_______", "____") → frac1Vinculum
  51. Text(If[a / b > c / d, ">", If[a / b < c / d, "<", "="]]) → relationshipSymbol
  52. Text(common_1) → equivFrac1Num
  53. Text(common_2) → equivFrac2Num
  54. Text(common_3) → equivFrac1Denom
  55. Text(common_3) → equivFrac2Denom
  56. Segment(BoxPt + (0.25, -2.5), BoxPt + (8.75, -2.5)) → relationshipWordsDivider
  57. Polygon(Corner[equivFrac1Denom, 1] + (-0.1, 0.1), Corner[equivFrac1Denom, 2] + (0.1, 0.1), (x(Corner[equivFrac1Denom, 2]) + 0.1, y(Corner[equivFrac1Num, 3])), (x(Corner[equivFrac1Denom, 1]) - 0.1, y(Corner[equivFrac1Num, 4]))) → equivFrac1Box, h_3, i_3, j_3, l_3
  58. Polygon(Corner[equivFrac2Denom, 1] + (-0.1, 0.1), Corner[equivFrac2Denom, 2] + (0.1, 0.1), (x(Corner[equivFrac2Denom, 2]) + 0.1, y(Corner[equivFrac2Num, 3])), (x(Corner[equivFrac2Denom, 1]) - 0.1, y(Corner[equivFrac2Num, 4]))) → equivFrac2Box, m_3, p_3, q_3, r_3
  59. Text(If[common_1 > 99 ∨ common_3 > 99, "__________", If[common_1 > 9 ∨ common_3 > 9, "_______", "____"]]) → equivFrac1Vinculum
  60. Text(If[common_2 > 99 ∨ common_3 > 99, "__________", If[common_2 > 9 ∨ common_3 > 9, "_______", "____"]]) → equivFrac2Vinculum
  61. Text("or") → equivFrac1Or
  62. Text("or") → equivFrac2Or
  63. Segment(Midpoint[G, N], Midpoint[H, M]) → areaModelDragLimit
  64. Point(areaModelDragLimit) → areaModelDragPt
  65. Segment((x(areaModelDragPt), y(N)), (x(areaModelDragPt), y(G))) → areaModelDragLine

AI Drawing Prompt Reference

Draw a horizontal number line with tick marks at both ends. Above the line, place two rectangular bars, each representing a fraction. Divide each bar into equal segments and shade a portion to indicate the numerator. Below each bar, draw vertical dashed lines aligning with the number line to show the fraction's position. Use alternating tick lengths on the number line for clarity. The layout should clearly compare the two fractions' magnitudes.
The prompt above was compiled from the original drawing commands and is for reference only.