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Visualizing Fraction Multiplication by edu-rordorfc

Visualizing Fraction Multiplication by edu-rordorfc
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2018-11-18 22:49
CirclePolygonFunctionSequence
① This GeoGebra example dynamically demonstrates fraction multiplication, using unit circles and grid polygons to show the geometric meaning of multiplying two fractions. ② Core math concepts include fraction multiplication, integers and fractions, area representation on the unit circle, with auxiliary use of linear equations and step functions. ③ Construction highlights: commands such as Segment, Point, Element, Max, Sequence, Polygon, FractionText, and If are used to build lists of denominators and numerators (denomList, numList), with objects like denom1-15, num1-15, and H-series points to adjust values interactively, and FractionText to display results. ④ Suitable for upper elementary to middle school students learning fraction multiplication, and for teachers to demonstrate the transition from visual intuition to symbolic computation.

GeoGebra Commands & Parameters

  1. Segment((0, 3), (4.8, 3)) → e
  2. Point(e) → H15
  3. Point(e) → H14
  4. Point(e) → H13
  5. Point(e) → H12
  6. Point(e) → H11
  7. Point(e) → H10
  8. Point(e) → H9
  9. Point(e) → H8
  10. Point(e) → H7
  11. Point(e) → H6
  12. Point(e) → H5
  13. Point(e) → H4
  14. Point(e) → H3
  15. Point(e) → H2
  16. Point(e) → H1
  17. Element(f2denom, ex) → d
  18. Element(f2num, ex) → c
  19. Element(f1num, ex) → a
  20. Element(f1denom, ex) → b
  21. Max(Sequence[If[Mod[(a * c), i] + Mod[(b * d), i] ≟ 0, i, -1], i, 1, Min[{(a * c), (b * d)}]]) → Simplified_{GCF}
  22. Sequence(A + (t * (B - A)), t, 0, 1, 1 / b) → L1
  23. Sequence(C + (t * (D - C)), t, 0, 1, 1 / b) → L2
  24. Segment(A, B) → c_1
  25. Segment(C, D) → d_1
  26. Sequence(Segment[Element[L1, k], Element[L2, k]], k, 2, b) → L5
  27. Element(dragPoint, ex) → H
  28. Segment(H, E) → f
  29. Segment(E, F) → g
  30. Segment(F, G) → h
  31. Segment(G, H) → i
  32. Segment(D, B) → j
  33. Segment(C, A) → k
  34. Element(L1, a + 1) → T1
  35. Element(L2, a + 1) → T2
  36. Polygon(A, T1, T2, C) → poly1, a_1, t1, t2, c_2
  37. Sequence(E + (t * (H - E)), t, 0, 1, 1 / d) → L3
  38. Sequence(F + (t * (G - F)), t, 0, 1, 1 / d) → L4
  39. Sequence(Segment[Element[L3, k], Element[L4, k]], k, 2, d) → L6
  40. Element(L3, c + 1) → T3
  41. Element(L4, c + 1) → T4
  42. Polygon(E, F, T4, T3) → poly2, e_1, f_1, t4, t3
  43. FractionText((Element[f1num, ex] * Element[f2num, ex] / ((Element[f1denom, ex] * Element[f2denom, ex])))) → simplText
  44. Element(numList, ex) → num
  45. Element(denomList, ex) → denom
  46. Polygon((0, 0), ((3 * Element[f1num, ex] / Element[f1denom, ex]), 0), ((3 * Element[f1num, ex] / Element[f1denom, ex]), (3 * Element[f2num, ex] / Element[f2denom, ex])), (0, (3 * Element[f2num, ex] / Element[f2denom, ex]))) → overlap, m, n, p, q
  47. If(bl, 0, 1) → black