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Fraction Comparer by Irina Boyadzhiev

Fraction Comparer by Irina Boyadzhiev
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2014-05-15 05:13
FunctionCoordinate GeometryGeometric ConstructionSlider Animation
In collections Fraction Skills FRACTIONS
This example demonstrates how to visually compare fractions and understand the impact of numerators and denominators on fraction values. Key math concepts include the fundamental properties of fractions, the roles of numerators and denominators, and their representation on a number line. Construction highlights the use of GeoGebra commands and objects like Ray, Point, Segment, Textfield, Sequence, Line, Append, If, Polygon, Zip, Distance, Vector, Translate, Corner, Element. Suitable for middle school and above students to deepen their understanding of fractions through experimentation.

GeoGebra Commands & Parameters

  1. Ray(A, X) → ray1
  2. Point(ray1) → B
  3. Segment(A, B) → a
  4. Segment(C, D) → b
  5. Textfield(n1) → inputBox1
  6. Textfield(d1) → inputBox2
  7. Textfield(n2) → inputBox3
  8. Textfield(d2) → inputBox4
  9. Sequence(A + ((i * a / d1) * UnitVector[a]), i, 1, d1) → list1
  10. Sequence(C + ((i * b / d2) * UnitVector[b]), i, 1, d2) → list2
  11. Segment(C, Element[list2, n2]) → d
  12. Segment(E, F) → e
  13. Segment(G, H) → f
  14. Sequence(E + ((i * e / n) * UnitVector[e]), i, 1, n) → list3
  15. Sequence(G + ((i * f / n) * UnitVector[f]), i, 1, n) → list4
  16. Sequence(Segment[Element[list3, i], Element[list4, i]], i, 1, n) → list5
  17. Line(E, G) → g
  18. Append(g, list5) → cuts
  19. If(Mod[n, d1] ≟ 0, true, false) → first
  20. If(Mod[n, d2] ≟ 0, true, false) → second
  21. Textfield(n1a) → inputBox5
  22. Textfield(d1a) → inputBox6
  23. Textfield(n2a) → n2s
  24. If((n1 * d1a) ≟ (d1 * n1a) ∧ Mod[d1a, LCM[d1, d2]] ≟ 0, true, false) → a1
  25. If((n2 * d2a) ≟ (d2 * n2a) ∧ Mod[d2a, LCM[d1, d2]] ≟ 0, true, false) → a2
  26. Textfield(d2a) → inputBox9
  27. If(first ∧ second, true, false) → s
  28. Polygon(A, B, 4) → poly1, h, i, j, k, Q, R
  29. Polygon(D, C, 4) → poly2, l, m, p, q, S, T
  30. Zip(Segment[Y, (x(Y), y(Y) + Distance[A, B])], Y, list1) → list6
  31. Polygon(A, Element[list1, n1], (x(Element[list1, n1]), y(Element[list1, n1]) + Distance[A, B]), R) → poly3, a_1, r, t, r_1
  32. Distance(A, B) → side
  33. Zip(Segment[Y, (x(Y), y(Y) - Distance[A, B])], Y, list2) → list7
  34. Polygon(C, Element[list2, n2], (x(Element[list2, n2]), y(Element[list2, n2]) - Distance[A, B]), S) → poly4, c, b_1, c_1, s_1
  35. Sequence(Line[Element[list3, i], Element[list4, i]], i, 1, n) → list8
  36. Sequence(S + ((i * b / d2) * UnitVector[b]), i, 1, d2) → list22
  37. Ray((1, 0), (10, 0)) → d_1
  38. Vector((0, 0), (0, -0.95)) → u
  39. Vector((0, 0), (0, 0.95)) → v
  40. Translate(a_1, Vector[(translate * u)]) → e_1
  41. Translate(c, Vector[(translate * v)]) → c'
  42. Corner(e_1, 2) → U
  43. Element(list1, n1) → end_e1
  44. Translate(end_e1, Vector[(translate * u)]) → EE
  45. Element(list2, n2) → End
  46. Translate(End, Vector[(translate * v)]) → EE2
  47. Sequence(R + ((i * a / d1) * UnitVector[a]), i, 1, d1 - 1 / d1) → list11
  48. Segment(V, W) → f_1
  49. Segment(Z, A_1) → g_1
  50. Point(f_1) → B_1

AI Drawing Prompt Reference

Draw two rays starting from the same point and extending in different directions, forming a line segment. Mark points on the segment corresponding to two input fractions and connect them to form two quadrilaterals. Also, draw line segments on a number line representing the two fractions and compare their lengths. Combine all these shapes to visually demonstrate the comparison of fractions and their fundamental properties.
The prompt above was compiled from the original drawing commands and is for reference only.